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Financial Arithmetic

138 questions

All types138Multiple choice70Numeric32Matching5Ordering3Fill in the blank28
Question 1Question →

A medical equipment technician is compensated with both an hourly wage and a tiered commission. The technician earns a base rate of 24.00perhourforastandard40−hourworkweek,andtime−and−a−halfforanyhoursworkedbeyond40.Additionally,thetechnicianearnsa624.00 per hour for a standard 40-hour workweek, and time-and-a-half for any hours worked beyond 40. Additionally, the technician earns a 6% commission on all service contracts sold up to 5,000 in a week, and an 8% commission on the portion of sales exceeding 5,000.Ifthetechnicianworked46hoursandsold5,000. If the technician worked 46 hours and sold 8,500 in service contracts last week, what were the technician's total gross earnings?

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Answer: $1,756.00

Answer

The technician's total gross earnings for the week were $1,756.00.
The correct answer is found by calculating each component of the compensation structure and summing them. Regular pay is 40 hours at 24.00/hour(24.00/hour ( 960.00). Overtime pay is 6 hours at the time-and-a-half rate of 36.00/hour(36.00/hour ( 216.00). The tiered commission is calculated as 6% of the first 5,000(5,000 ( 300.00) plus 8% of the remaining 3,500insales(3,500 in sales ( 280.00). Adding these components together (960.00+960.00 + 216.00 + 300.00+300.00 + 280.00) results in total gross earnings of $1,756.00.

Step-by-Step Solution

1
Calculate the regular base pay.
40 hours \times 24.00/hour=24.00/hour = 960.00
The technician is paid the base rate for the first 40 hours worked.
2
Calculate the overtime pay.
6 hours \times (24.00×1.5)=6×24.00 \times 1.5) = 6 \times 36.00 = $216.00
The 6 hours worked beyond the standard 40 hours are paid at time-and-a-half.
3
Calculate the first tier of commission.
5,000×0.06=5,000 \times 0.06 = 300.00
The technician earns a 6% commission on the first $5,000 of service contracts sold.
4
Calculate the second tier of commission.
(8,500−8,500 - 5,000) \times 0.08 = 3,500×0.08=3,500 \times 0.08 = 280.00
The technician earns an 8% commission on any sales amount exceeding the initial $5,000.
5
Calculate total gross earnings.
960.00+960.00 + 216.00 + 300.00+300.00 + 280.00 = $1,756.00
Total gross earnings are the sum of regular pay, overtime pay, and all commission tiers.

Key Concept

Calculating gross earnings involving overtime premiums and multi-tiered commission structures.
Question 2Question →

A specialized equipment technician earns a base wage of 28.00perhourforastandard40−hourworkweek,withanyadditionalhourspaidattime−and−a−half.Thetechnicianalsoearnsatieredcommissiononequipmentsold:428.00 per hour for a standard 40-hour workweek, with any additional hours paid at time-and-a-half. The technician also earns a tiered commission on equipment sold: 4% on the first 10,000 of sales, and a higher commission rate on all sales beyond $10,000.

Last week, the technician worked 48 hours, sold 30,000worthofequipment,andhadtotalgrossearningsof30,000 worth of equipment, and had total gross earnings of 3,056.

Calculate the commission rate for the sales exceeding $10,000.

Fill in the blanks below

The commission rate on sales exceeding $10,000 is %.
Show answer & explanation

Answer

The commission rate on sales exceeding $10,000 is 6%.
The correct answer is found by first isolating the total commission earned (3,056gross−3,056 gross - 1,456 wages = 1,600commission).Then,subtractthe1,600 commission). Then, subtract the 400 earned from the first 10,000tier.Thisleaves10,000 tier. This leaves 1,200 in commission earned on the remaining 20,000insales.Dividing20,000 in sales. Dividing 1,200 by $20,000 yields a 0.06 or 6% commission rate.

Step-by-Step Solution

1
Calculate the base pay for standard hours.
$1,120
The first 40 hours are paid at the standard rate: 40 hours × $28.00/hour.
2
Calculate the overtime pay.
$336
The overtime rate is 28.00×1.5=28.00 × 1.5 = 42.00/hour. The technician worked 8 overtime hours (48 - 40). 42.00×8=42.00 × 8 = 336.
3
Calculate the total hourly wages.
$1,456
Add the base pay and overtime pay: 1,120+1,120 + 336 = $1,456.
4
Calculate the total commission earned.
$1,600
Subtract the total hourly wages from the total gross earnings: 3,056−3,056 - 1,456 = $1,600.
5
Calculate the tier 1 commission amount.
$400
The commission is 4% on the first 10,000ofsales:10,000 of sales: 10,000 × 0.04 = $400.
6
Calculate the tier 2 commission amount and tier 2 sales volume.
Tier 2 Commission: 1,200.Tier2Sales:1,200. Tier 2 Sales: 20,000.
Subtract tier 1 commission from total commission (1,600−1,600 - 400 = 1,200).Subtracttier1salesfromtotalsales(1,200). Subtract tier 1 sales from total sales ( 30,000 - 10,000=10,000 = 20,000).
7
Determine the tier 2 commission rate.
6%
Divide the tier 2 commission by the tier 2 sales volume: 1,200÷1,200 ÷ 20,000 = 0.06, which is 6%.

Key Concept

Reverse engineering multi-tier compensation structures involving overtime wages and graduated commission rates.
Question 3Question →

A sales representative earns a base monthly salary of 2,400.Theyalsoearnacommissionbasedontheirtotalmonthlysalesvolume.Thecommissionstructureisasfollows:−2,400. They also earn a commission based on their total monthly sales volume. The commission structure is as follows: - 4\%onthefirst on the first 15,000 of sales
- 6%6\% on the next 25,000ofsales−25,000 of sales - 8.5\%onanysalesexceeding on any sales exceeding 40,000

In addition, if their total monthly sales exceed 50,000,theyreceiveaone−timeperformancebonusof50,000, they receive a one-time performance bonus of 750. Last month, the representative had a total sales volume of $54,200. What was the representative's total gross income for the month?

Show answer & explanation

Answer: 6457

Answer

6457
The correct gross income is found by calculating the commission for each tier separately (600forthefirsttier,600 for the first tier, 1,500 for the second tier, and 1,207forthethirdtier),summingthemtogetatotalcommissionof1,207 for the third tier), summing them to get a total commission of 3,307, and then adding the base salary of 2,400andthe2,400 and the 750 performance bonus (awarded since sales exceeded 50,000)forafinaltotalof50,000) for a final total of 6,457.

Step-by-Step Solution

1
Calculate the commission for the first tier (0to0 to 15,000).
15,000×0.04=15,000 \times 0.04 = 600
The representative earns a 4% commission on the first $15,000 of sales.
2
Calculate the commission for the second tier (the next $25,000).
25,000×0.06=25,000 \times 0.06 = 1,500
The 6% rate applies to the next 25,000ofsales(coveringsalesfrom25,000 of sales (covering sales from 15,000 to $40,000).
3
Calculate the commission for the third tier (sales exceeding $40,000).
54,200−54,200 - 40,000 = 14,200.14,200. 14,200 \times 0.085 = $1,207
The 8.5% rate applies to any sales exceeding the $40,000 threshold.
4
Sum the total commission.
600+600 + 1,500 + 1,207=1,207 = 3,307
Adding the amounts from all three tiers gives the total commission earned.
5
Calculate the total gross income by adding the base salary, total commission, and the performance bonus.
2,400+2,400 + 3,307 + 750=750 = 6,457
Total sales (54,200)exceededthe54,200) exceeded the 50,000 threshold, so the $750 bonus is awarded. Gross income includes base pay, total commission, and the bonus.

Key Concept

Calculating tiered commissions, applying percentages to multiple thresholds, and combining various income streams.
Question 4Question →

A rare book dealer recorded the financial details for four different inventory items. Match each item's transaction history to its final profit or loss percentage.

Click a left item, then click its matching right item

Items

First edition novel: purchased for $120\$120 and sold for $150\$150
Antique atlas: purchased for $300\$300, plus $100\$100 for restoration, and sold for $320\$320
Signed biography: purchased for $60\$60 and sold for $90\$90
Vintage encyclopedias: purchased for $80\$80 and sold for $72\$72

Matches

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Answer

The transactions match their respective percentages by dividing the net dollar profit or loss by the total initial cost.
Each correct pair accurately reflects the percentage change from the initial total investment. The total cost always serves as the base (denominator) for these percentage calculations.

Step-by-Step Solution

1
Calculate the profit percentage for the first edition novel.
Profit is $150−$120=$30\$150 - \$120 = \$30. Percentage is 30120=25%\frac{30}{120} = 25\%.
To find the profit percentage, divide the absolute profit by the original purchase cost.
2
Calculate the total cost and loss percentage for the antique atlas.
Total cost is $300+$100=$400\$300 + \$100 = \$400. Loss is $400−$320=$80\$400 - \$320 = \$80. Percentage is 80400=20%\frac{80}{400} = 20\%.
Overhead and restoration costs must be added to the purchase price to determine the true initial cost.
3
Calculate the profit percentage for the signed biography.
Profit is $90−$60=$30\$90 - \$60 = \$30. Percentage is 3060=50%\frac{30}{60} = 50\%.
Dividing the absolute profit by the initial cost provides the correct percentage.
4
Calculate the loss percentage for the vintage encyclopedias.
Loss is $80−$72=$8\$80 - \$72 = \$8. Percentage is 880=10%\frac{8}{80} = 10\%.
Dividing the dollar loss by the original cost yields the correct loss percentage.

Key Concept

Calculating profit and loss percentages by dividing the net financial change by the total initial cost, ensuring all overhead is included.
Question 5Question →

A base logistics officer needs to requisition 1,500 feet of paracord. Distributor A sells a 100-yard spool of paracord for 36.00.DistributorBsellsthesameparacordina50−footrollfor36.00. Distributor B sells the same paracord in a 50-foot roll for 5.50. If the officer purchases the entire 1,500 feet from the distributor with the lower overall cost, how much total money will be saved compared to purchasing from the more expensive distributor?

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Answer: $15.00

Answer

The total savings is $15.00 when purchasing from Distributor B instead of Distributor A.
The correct answer is found by equalizing the units and calculating the total cost required to obtain 1,500 feet from each distributor. Distributor A provides 300 feet (100 yards) per 36.00spool,so5spoolsareneeded,costing36.00 spool, so 5 spools are needed, costing 180.00. Distributor B provides 50 feet per 5.50roll,so30rollsareneeded,costing5.50 roll, so 30 rolls are needed, costing 165.00. The total savings is the difference: 180.00−180.00 - 165.00 = $15.00.

Step-by-Step Solution

1
Calculate the total cost if buying from Distributor A.
100 yards × 3 feet/yard = 300 feet per spool. Number of spools needed = 1,500 feet ÷ 300 feet/spool = 5 spools. Total cost = 5 × 36.00=36.00 = 180.00.
Units must be consistent (feet) to compare or fulfill the 1,500-foot requirement accurately.
2
Calculate the total cost if buying from Distributor B.
Number of rolls needed = 1,500 feet ÷ 50 feet/roll = 30 rolls. Total cost = 30 × 5.50=5.50 = 165.00.
We must find the exact total cost for fulfilling the entire requisition of 1,500 feet with the second option.
3
Find the difference between the two total costs to determine savings.
180.00−180.00 - 165.00 = $15.00.
Subtracting the lower cost from the higher cost reveals the total amount saved.

Key Concept

Comparing unit prices across different bulk packages by establishing a common metric or total purchasing cost.
Question 6Question →

A bakery owner purchases a commercial oven for $2,400\$2,400. She pays $250\$250 for freight shipping and $150\$150 for professional installation. If she later sells the oven for a 15%15\% loss on her total initial investment, what is the selling price in dollars?

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Answer: 2380

Answer

2380
The correct answer is found by first determining the total investment ($2,400+$250+$150=$2,800\$2,400 + \$250 + \$150 = \$2,800), then finding the 15%15\% loss (0.15×$2,800=$4200.15 \times \$2,800 = \$420), and finally subtracting that loss from the total investment to get the selling price ($2,800−$420=$2,380\$2,800 - \$420 = \$2,380).

Step-by-Step Solution

1
Calculate the total initial investment.
$2,400+$250+$150=$2,800\$2,400 + \$250 + \$150 = \$2,800
All overhead costs must be added to the purchase price to find the true total cost.
2
Calculate the dollar amount of the 15%15\% loss.
0.15×$2,800=$4200.15 \times \$2,800 = \$420
The loss is based on the total initial investment, not just the purchase price.
3
Determine the final selling price.
$2,800−$420=$2,380\$2,800 - \$420 = \$2,380
Subtracting the loss amount from the total investment gives the selling price.

Key Concept

Calculating total cost including overhead, and applying a percentage loss to find the final selling price.

Alternative Method

Instead of calculating the loss and subtracting it, you can multiply the total investment by 85%85\% (since 100%−15%=85%100\% - 15\% = 85\%). 0.85×$2,800=$2,3800.85 \times \$2,800 = \$2,380.
Estimated Time:1m 0s
Question 7Question →

A motor pool mechanic needs to buy spark plugs. A single spark plug costs 3.00.Aboxofonedozensparkplugscosts3.00. A box of one dozen spark plugs costs 24.00. How much money is saved per spark plug by purchasing the box instead of buying them individually?

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Answer: $1.00

Answer

$1.00
Purchasing the box of one dozen means buying 12 spark plugs for 24.00,whichresultsinaunitpriceof24.00, which results in a unit price of 2.00 each (24.00÷12).Buyingthemindividuallycosts24.00 ÷ 12). Buying them individually costs 3.00 each. The difference per spark plug is 3.00−3.00 - 2.00 = $1.00.

Step-by-Step Solution

1
Determine the total number of items in the box.
1 dozen = 12 spark plugs.
To find the cost of a single spark plug from the box, the total quantity is required.
2
Calculate the unit price of a spark plug from the box.
24.00÷12=24.00 ÷ 12 = 2.00 per spark plug.
Dividing the total cost by the quantity yields the price per individual item.
3
Calculate the savings per spark plug.
3.00−3.00 - 2.00 = $1.00.
Subtracting the bulk unit price from the individual unit price gives the savings per item.

Key Concept

Unit Price Comparisons
Question 8Question →

Match each landscaping supply transaction to its correct final profit or loss percentage.

Click a left item, then click its matching right item

Items

Purchased a soil pallet for 200andsolditfor200 and sold it for 250.
Bought a used lawnmower for 400,spent400, spent 100 on repairs, and sold it for $400.
Acquired a set of gardening tools for 150andsoldthemonclearancefor150 and sold them on clearance for 90.
Purchased decorative stones for 300andsoldthemfor300 and sold them for 600.

Matches

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Answer

The soil pallet transaction resulted in a 25% profit. The lawnmower transaction resulted in a 20% loss. The gardening tools transaction resulted in a 40% loss. The decorative stones transaction resulted in a 100% profit.
Each matching pair accurately reflects the transaction's net profit or loss divided by the total initial cost (including any overhead).

Step-by-Step Solution

1
Calculate the percentage profit for the soil pallet.
Profit = 250−250 - 200 = 50.Percentage=(50. Percentage = ( 50 / $200) * 100 = 25%. This matches the '25% profit' option.
Profit is the positive difference between the selling price and cost. The percentage is always calculated over the original cost.
2
Determine the total initial cost of the lawnmower including overhead, then find the percentage loss.
Total cost = 400+400 + 100 = 500.Loss=500. Loss = 500 - 400=400 = 100. Percentage = (100/100 / 500) * 100 = 20%. This matches the '20% loss' option.
Overhead expenses (like repairs) must be added to the initial purchase price to find the true total cost basis before evaluating profit or loss.
3
Calculate the percentage loss for the gardening tools.
Loss = 150−150 - 90 = 60.Percentage=(60. Percentage = ( 60 / $150) * 100 = 40%. This matches the '40% loss' option.
Loss is the negative difference between the selling price and cost, and the percentage is found by dividing that difference by the original cost.
4
Calculate the percentage profit for the decorative stones.
Profit = 600−600 - 300 = 300.Percentage=(300. Percentage = ( 300 / $300) * 100 = 100%. This matches the '100% profit' option.
When an item is sold for exactly double its purchase price, the profit equals the original cost, which corresponds to a 100% return.

Key Concept

Calculating percentage profit and loss based on total cost

Alternative Method

For profit scenarios, you can divide the selling price directly by the cost price to get a multiplier. For the decorative stones: 600/600 / 300 = 2.0. A multiplier of 2.0 corresponds to a 100% increase (profit).
Estimated Time:1m 30s
Question 9Question →

Read the compensation scenario below and fill in the blanks with the correct numerical values.

Fill in the blanks below

A salon stylist earns a weekly base salary of 450.Shealsoreceivesa20450. She also receives a 20% commission on all chemical treatments and a 10% commission on retail product sales. In a single week, she bills 850 for chemical treatments and sells 240inretailproducts.Forthisweek,thestylistearnedatotalof240 in retail products. For this week, the stylist earned a total of in commissions, which brings her total gross pay to $.
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Answer

The stylist earned 194intotalcommissions,makinghertotalgrosspay194 in total commissions, making her total gross pay 644.
The correct commission is found by multiplying each sales category by its respective percentage (850×0.20=170850 \times 0.20 = 170 and 240×0.10=24240 \times 0.10 = 24), summing them (170+24=194170 + 24 = 194), and adding the result to the 450basesalaryforatotalof450 base salary for a total of 644.

Step-by-Step Solution

1
Calculate the commission earned from chemical treatments.
850×0.20=170850 \times 0.20 = 170
The stylist earns 20% commission on the $850 billed for these specific services.
2
Calculate the commission earned from retail product sales.
240×0.10=24240 \times 0.10 = 24
The stylist earns 10% commission on the $240 worth of retail sales.
3
Determine the total commission earned for the week.
170+24=194170 + 24 = 194
Total commission is the sum of the commissions from both categories.
4
Calculate the total gross pay.
450+194=644450 + 194 = 644
Total gross pay is the base salary plus the total commission earned.

Key Concept

Calculating varied commission rates on different sales categories and combining them with a base salary to find gross earnings.
Estimated Time:1m 30s
Question 10Question →

A hospital administrator places $12,000\$12,000 into a fixed-term savings certificate that earns an annual simple interest rate of 4.2%4.2\%. If no other deposits or withdrawals are made, what is the total accumulated balance, in dollars, of the certificate after exactly 30 months?

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Answer: 13260

Answer

The total accumulated balance is 13260.
The correct answer is found by first converting the 30-month time period into 2.5 years (30÷12=2.530 \div 12 = 2.5), and the 4.2%4.2\% interest rate into the decimal 0.0420.042 (4.2÷100=0.0424.2 \div 100 = 0.042). Using the simple interest formula I=P×R×TI = P \times R \times T, the interest earned is $12,000×0.042×2.5=$1,260\$12,000 \times 0.042 \times 2.5 = \$1,260. Adding this interest to the original principal of $12,000\$12,000 gives a total accumulated balance of $13,260\$13,260.

Step-by-Step Solution

1
Convert the interest rate to a decimal and the time period to years.
R=4.2%=0.042R = 4.2\% = 0.042, and T=30 months÷12 months/year=2.5 yearsT = 30 \text{ months} \div 12 \text{ months/year} = 2.5 \text{ years}.
The standard simple interest formula requires the interest rate as a decimal and the time expressed in years.
2
Calculate the total interest earned using the simple interest formula I=P×R×TI = P \times R \times T.
I=12000×0.042×2.5=1260I = 12000 \times 0.042 \times 2.5 = 1260
This determines how much additional money the certificate earns over the 30-month period.
3
Calculate the total accumulated balance by adding the interest earned to the original principal.
Total Balance = 12000+1260=1326012000 + 1260 = 13260
The question asks for the total accumulated balance, which includes both the initial deposit (principal) and the earned interest.

Key Concept

Calculating simple interest over a fractional year and determining the total accumulated amount.
Question 11Question →

Determine the total gross earnings for the month based on the given compensation structure.

Fill in the blanks below

During the month of October, a medical equipment consultant recorded total sales of $45,000\$45,000. His compensation package includes a guaranteed monthly base salary of $1,200\$1,200. On top of this base, he earns a 5%5\% commission on the first $20,000\$20,000 of his sales, and an 8%8\% commission on all sales volume beyond that initial $20,000\$20,000. Based on these figures, the consultant's total gross pay for October is $\$$.
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Answer

The consultant's total gross pay is $4,200.
The total gross pay is found by isolating the sales into two tiers: the first 20,000earnsa520,000 earns a 5% commission ( 1,000) and the remaining 25,000earnsan825,000 earns an 8% commission ( 2,000). Adding these two commissions to the 1,200basesalaryyieldsatotalgrosspayof1,200 base salary yields a total gross pay of 4,200.

Step-by-Step Solution

1
Calculate the commission earned on the first tier of sales.
$20,000×0.05=$1,000\$20,000 \times 0.05 = \$1,000
The consultant earns a 5% commission on the initial $20,000 of sales.
2
Determine the amount of sales that qualify for the second commission tier.
$45,000−$20,000=$25,000\$45,000 - \$20,000 = \$25,000
The higher commission rate only applies to the sales volume exceeding the first $20,000.
3
Calculate the commission earned on the second tier of sales.
$25,000×0.08=$2,000\$25,000 \times 0.08 = \$2,000
The consultant earns an 8% commission on the remaining $25,000 of sales.
4
Sum the base salary and both commission amounts to find the total gross pay.
$1,200+$1,000+$2,000=$4,200\$1,200 + \$1,000 + \$2,000 = \$4,200
Total earnings are the sum of the guaranteed salary and all commissions earned.

Key Concept

Calculating total earnings involving a base salary and a multi-tiered commission structure.
Question 12Question →

A civil engineer needs to earn exactly $840\$840 in simple interest over a 1010-month period to offset the cost of new drafting software. If a local credit union offers a business savings account with a 4.8%4.8\% annual simple interest rate, how much principal must be deposited into the account?

Show answer & explanation

Answer: $21,000\$21,000

Answer

The correct principal amount to deposit is $21,000\$21,000.
The correct answer accurately uses the simple interest formula by first converting the 10-month period into a fraction of a year (10/1210/12 or 5/65/6). Multiplying the annual rate of 0.0480.048 by 5/65/6 yields 0.040.04. Dividing the target interest of $840\$840 by 0.040.04 correctly determines the required principal.

Step-by-Step Solution

1
Identify the known variables from the problem.
Interest (II) = $840\$840, annual rate (rr) = 4.8%=0.0484.8\% = 0.048, and time (tt) = 1010 months.
Organizing the given information clarifies what is needed for the simple interest formula.
2
Convert the time period from months to years because the interest rate is an annual rate.
t=1012=56 yearst = \frac{10}{12} = \frac{5}{6} \text{ years}
Standard simple interest formulas require time to be in the same unit as the rate.
3
Substitute the values into the simple interest formula I=P×r×tI = P \times r \times t to set up the equation.
840=P×0.048×56840 = P \times 0.048 \times \frac{5}{6}
This establishes the mathematical relationship to isolate the unknown principal amount (PP).
4
Simplify the equation and solve for the principal.
840=P×0.04⇒P=8400.04=21000840 = P \times 0.04 \Rightarrow P = \frac{840}{0.04} = 21000
Dividing both sides by the calculated coefficient isolates PP and yields the final answer.

Key Concept

Solving for Principal using the Simple Interest Formula
Question 13Question →

An independent contractor installs smart home systems. He earns a base rate of $18.50\$18.50 per hour for a standard 4040-hour workweek. For any overtime hours worked beyond 4040 hours, he earns time-and-a-half. He also receives a 5%5\% commission on all equipment sales he makes. If he worked 4848 hours this week and sold $3,200\$3,200 worth of equipment, what are his total gross earnings for the week?

Show answer & explanation

Answer: \$1,122.00

Answer

The total gross earnings for the week are $1,122.00\$1,122.00.
The correct answer accurately accounts for all three payment streams. The base pay for 40 hours is 40×$18.50=$740.0040 \times \$18.50 = \$740.00. The overtime pay for the 8 extra hours is calculated at time-and-a-half (18.50×1.5=$27.75/hr18.50 \times 1.5 = \$27.75/hr), which yields 8×$27.75=$222.008 \times \$27.75 = \$222.00. The 5% commission on $3,200\$3,200 in sales is 0.05×3,200=$160.000.05 \times 3,200 = \$160.00. Adding these together ($740+$222+$160\$740 + \$222 + \$160) results in $1,122.00\$1,122.00.

Step-by-Step Solution

1
Calculate the standard base pay for 4040 hours.
40×$18.50=$740.0040 \times \$18.50 = \$740.00
The contractor earns a fixed hourly rate for the first 40 hours worked.
2
Calculate the number of overtime hours and the overtime rate.
Overtime hours: 48−40=848 - 40 = 8. Overtime rate: $18.50×1.5=$27.75\$18.50 \times 1.5 = \$27.75.
Overtime is paid at 'time-and-a-half' for any hours worked beyond the standard 40 hours.
3
Calculate the total overtime pay.
8×$27.75=$222.008 \times \$27.75 = \$222.00
Multiply the overtime hours by the higher overtime pay rate.
4
Calculate the commission earned on equipment sales.
0.05×$3,200=$160.000.05 \times \$3,200 = \$160.00
The commission is 5% (or 0.05) of the total sales volume.
5
Sum all three components to find the total gross earnings.
$740.00+$222.00+$160.00=$1,122.00\$740.00 + \$222.00 + \$160.00 = \$1,122.00
Gross earnings are the sum of base pay, overtime pay, and commission before any deductions.

Key Concept

Calculating Gross Pay with Overtime and Commission
Question 14Question →

Calculate the missing financial values for the equipment purchase described below.

Fill in the blanks below

A veterinary clinic is purchasing a new digital ultrasound machine originally listed at $6,500\$6,500. The medical supplier is offering a 20%20\% promotional discount. Because the clinic agrees to pick up the equipment themselves, they receive an additional 5%5\% discount off the already reduced price.

The total discount amount the clinic receives is $\$andthefinalpricepaidforthemachineis and the final price paid for the machine is \$$.
Show answer & explanation

Answer

The total discount amount is 1,560andthefinalpriceis1,560 and the final price is 4,940.
The first discount of 20% saves 1,300,bringingthepricedownto1,300, bringing the price down to 5,200. The second discount of 5% applies to this new 5,200balance,savinganadditional5,200 balance, saving an additional 260. Subtracting the second discount from 5,200yieldsafinalpriceof5,200 yields a final price of 4,940. The total amount saved combines both discounts: 1,300+1,300 + 260 = $1,560.

Step-by-Step Solution

1
Calculate the amount of the first discount.
$1,300
Multiply the original price ($6,500) by the first discount rate (20% or 0.20).
2
Calculate the price after the first discount.
$5,200
Subtract the first discount (1,300)fromtheoriginalprice(1,300) from the original price ( 6,500).
3
Calculate the amount of the second discount.
$260
Multiply the reduced price ($5,200) by the additional discount rate (5% or 0.05).
4
Determine the final price.
$4,940
Subtract the second discount (260)fromthepreviouslyreducedprice(260) from the previously reduced price ( 5,200).
5
Determine the total discount amount.
$1,560
Add the first discount (1,300)andtheseconddiscount(1,300) and the second discount ( 260).

Key Concept

Successive Discounts
Question 15Question →

An armory quartermaster is ordering gun solvent for weapons maintenance. The solvent is available in four different packaging options. Arrange the options from the lowest price per gallon to the highest price per gallon.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct order from lowest to highest price per gallon is: 2-quart bottle, 5-gallon bucket, 4-gallon case, 1-pint bottle.
By converting all package volumes into gallons, we can compare their unit prices accurately. The 22-quart bottle costs $12.00\$12.00 per gallon, the 55-gallon bucket costs $13.00\$13.00 per gallon, the 44-gallon case costs $13.50\$13.50 per gallon, and the 11-pint bottle costs $14.00\$14.00 per gallon. Arranging them from lowest to highest yields this sequence.

Step-by-Step Solution

1
Calculate the unit price for the 22-quart bottle.
$12.00\$12.00 per gallon
There are 44 quarts in a gallon, making 22 quarts equivalent to 0.50.5 gallons. $6.00÷0.5=$12.00\$6.00 \div 0.5 = \$12.00 per gallon.
2
Calculate the unit price for the 55-gallon bucket.
$13.00\$13.00 per gallon
Dividing the total cost by the number of gallons: $65.00÷5=$13.00\$65.00 \div 5 = \$13.00 per gallon.
3
Calculate the unit price for the 44-gallon case.
$13.50\$13.50 per gallon
Dividing the total cost by the number of gallons: $54.00÷4=$13.50\$54.00 \div 4 = \$13.50 per gallon.
4
Calculate the unit price for the 11-pint bottle.
$14.00\$14.00 per gallon
There are 88 pints in a gallon. Multiplying the pint price by 88 gives the gallon price: $1.75×8=$14.00\$1.75 \times 8 = \$14.00 per gallon.
5
Order the unit prices from lowest to highest.
$12.00\$12.00, $13.00\$13.00, $13.50\$13.50, $14.00\$14.00
The question asks for the options to be arranged in ascending order based on their price per gallon.

Key Concept

Converting various liquid volume measurements to a common unit (gallons) in order to accurately compare unit prices.
Question 16Question →

A vendor purchases a vintage jacket for 6060 dollars and later sells it at a market for 7575 dollars. What is the vendor's profit percentage on this item?

Show answer & explanation

Answer: 25%25\%

Answer

The vendor's profit percentage is 25%25\%.
The total profit is found by subtracting the cost price (6060) from the selling price (7575), resulting in a 1515 dollar profit. To find the profit percentage, you must divide the profit by the original cost price (15÷60=0.2515 \div 60 = 0.25). Converting the decimal 0.250.25 to a percentage gives 25%25\%.

Step-by-Step Solution

1
Calculate the dollar amount of the profit.
75−60=1575 - 60 = 15
Profit is the difference between the selling price and the cost price.
2
Divide the profit by the original cost price.
1560=0.25\frac{15}{60} = 0.25
Profit percentage is based on the original cost, not the final selling price.
3
Convert the resulting decimal to a percentage.
0.25×100=25%0.25 \times 100 = 25\%
The question asks for the final answer in percentage format.

Key Concept

Calculating profit percentage using the original cost as the base value.
Estimated Time:45s
Question 17Question →

A family goes out for dinner, and the total cost of their meal is $85.00\$85.00. They use a coupon for 20%20\% off the cost of the meal. A sales tax of 8%8\% is applied to the discounted price. They also decide to leave a 15%15\% tip based on the original pre-discount cost of the meal. What is the total amount the family paid?

Show answer & explanation

Answer: $86.19\$86.19

Answer

The total amount the family paid is $86.19\$86.19.
The correct answer accurately separates the bases for the different percentage calculations. The 20%20\% discount reduces the $85.00\$85.00 meal to $68.00\$68.00. The 8%8\% tax is applied to that $68.00\$68.00 base, adding $5.44\$5.44. The 15%15\% tip is calculated on the original $85.00\$85.00 base, adding $12.75\$12.75. The sum of the discounted meal, tax, and tip is $68.00+$5.44+$12.75=$86.19\$68.00 + \$5.44 + \$12.75 = \$86.19.

Step-by-Step Solution

1
Calculate the discount amount and the new discounted price of the meal.
20%20\% of $85.00=0.20×85=$17.00\$85.00 = 0.20 \times 85 = \$17.00. The discounted price is $85.00−$17.00=$68.00\$85.00 - \$17.00 = \$68.00.
The coupon provides a 20%20\% discount on the original meal cost, which must be deducted before applying the sales tax.
2
Calculate the sales tax based on the discounted price.
8%8\% of $68.00=0.08×68=$5.44\$68.00 = 0.08 \times 68 = \$5.44.
The problem states that the sales tax is applied to the discounted price, not the original price.
3
Calculate the tip based on the original pre-discount cost.
15%15\% of $85.00=0.15×85=$12.75\$85.00 = 0.15 \times 85 = \$12.75.
The problem explicitly states that the tip is based on the original pre-discount cost of the meal.
4
Add the discounted price, the sales tax, and the tip to find the total amount paid.
$68.00+$5.44+$12.75=$86.19\$68.00 + \$5.44 + \$12.75 = \$86.19.
The final total is the sum of the actual cost of the meal, the required tax, and the gratuity.

Key Concept

Calculating multi-step financial arithmetic involving discounts, taxes, and tips, ensuring each percentage is applied to the correct base amount.
Question 18Question →

Read the scenario and perform the necessary calculations. Enter the exact numerical values in the blanks.

Fill in the blanks below

A customer purchases a premium spa package for $250.00\$250.00. The local municipality applies a 6%6\% sales tax to the base price of all spa services. After the tax is added, the customer decides to leave a 20%20\% tip based on the new, post-tax total on the receipt.

The amount of the tip is $\$andthefinaltotalcostpaidbythecustomeris and the final total cost paid by the customer is \$$.
Show answer & explanation

Answer

The amount of the tip is 53 (or 53.00) and the final total cost is 318 (or 318.00).
The correct amounts are found by sequentially applying the percentages according to the narrative. First, a 6%6\% tax on the $250.00\$250.00 base price adds $15.00\$15.00, resulting in a $265.00\$265.00 subtotal. The 20%20\% tip is then applied to this $265.00\$265.00 subtotal, resulting in a $53.00\$53.00 tip. Adding this tip to the subtotal gives the final cost of $318.00\$318.00.

Step-by-Step Solution

1
Calculate the sales tax amount on the base price.
$15.00\$15.00
Multiply the base price ($250.00\$250.00) by the tax rate (0.060.06).
2
Determine the post-tax total.
$265.00\$265.00
Add the tax amount ($15.00\$15.00) to the base price ($250.00\$250.00) to find the amount upon which the tip will be calculated.
3
Calculate the tip amount.
$53.00\$53.00
Multiply the post-tax total ($265.00\$265.00) by the tip rate (0.200.20).
4
Calculate the final total cost.
$318.00\$318.00
Add the tip amount ($53.00\$53.00) to the post-tax total ($265.00\$265.00).

Key Concept

Calculating sales tax on a base price and applying a tip percentage to the sequential post-tax total.
Question 19Question →

Match each buy-and-sell transaction to the correct dollar amount of profit or loss.

Click a left item, then click its matching right item

Items

Buy a tool set for $40\$40 and sell it for $65\$65.
Buy a used guitar for $200\$200 and sell it for $150\$150.
Buy a blender for $30\$30 and sell it for $30\$30.
Buy a winter coat for $85\$85 and sell it for $100\$100.

Matches

Show answer & explanation

Answer

Tool set matches $25\$25 Profit; Guitar matches $50\$50 Loss; Blender matches $0\$0 (Break-even); Winter coat matches $15\$15 Profit.
Profit is correctly calculated when the selling price is higher than the cost price. A loss occurs when the selling price is lower than the cost price, and breaking even occurs when the two prices are identical.

Step-by-Step Solution

1
Calculate the difference between the selling price and the cost price for each transaction.
Tool set: $65−$40=$25\$65 - \$40 = \$25. Guitar: $150−$200=−$50\$150 - \$200 = -\$50. Blender: $30−$30=$0\$30 - \$30 = \$0. Coat: $100−$85=$15\$100 - \$85 = \$15.
The difference determines the amount of money gained or lost on each item.
2
Determine if each result is a profit, loss, or break-even.
Positive values ($25\$25, $15\$15) are profits. The negative value (−$50-\$50) is a loss. Zero ($0\$0) is a break-even.
A positive difference means money was made (profit), a negative difference means money was lost (loss), and zero means no change in value.

Key Concept

Calculating absolute profit or loss by finding the difference between selling price and cost price.
Question 20Question →

A landscaper purchases a used backpack leaf blower for 240.Aweeklater,theyselltheequipmenttoanothercontractorfor240. A week later, they sell the equipment to another contractor for 300. What is the landscaper's profit percentage?

Show answer & explanation

Answer: 25%

Answer

25%
To find the profit percentage, first calculate the total profit by subtracting the cost (240)fromthesellingprice(240) from the selling price ( 300), which equals 60.Then,dividethatprofitbytheoriginalcost(60. Then, divide that profit by the original cost ( 240). 60dividedby60 divided by 240 is 0.25, which translates to a 25% profit.

Step-by-Step Solution

1
Determine the dollar amount of the profit by subtracting the original purchase price from the selling price.
300−300 - 240 = $60
Profit is the positive difference between revenue (selling price) and expenses (cost price).
2
Set up a fraction or division problem placing the profit over the original cost price.
60 / 240
Profit percentage is always calculated relative to the original cost, not the final selling price.
3
Simplify the fraction and convert it into a percentage.
60 / 240 = 1 / 4 = 0.25 = 25%
Converting the decimal ratio to a percentage provides the final answer.

Key Concept

Profit Percentage Calculation

Alternative Method

You can also solve this by dividing the selling price by the cost price first (300/300 / 240 = 1.25). Because 1.00 represents the original 100% cost, the decimal portion remaining (0.25) represents the profit, which is 25%.
Estimated Time:45s
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Financial Arithmetic Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB) | Examkin