Financial Arithmetic

138 questions

Question 41Question →

A freelance illustrator earns a fixed weekly retainer of $400\$400 and receives a 10%10\% commission on any artwork sold in galleries. If the illustrator sells $1,500\$1,500 worth of artwork during the week, what is their total gross pay for that week?

Show answer & explanation

Answer: $550\$550

Answer

The total gross pay is $550\$550.
To find the total gross pay, first calculate 10% of the $1,500\$1,500 in sales, which is $150\$150. Then, add this commission amount to the $400\$400 fixed retainer, resulting in a total gross pay of $550\$550.

Step-by-Step Solution

1
Calculate the commission earned from the artwork sales.
$1,500×0.10=$150\$1,500 \times 0.10 = \$150
The illustrator earns a 10% commission on the total value of artwork sold.
2
Add the earned commission to the fixed weekly retainer to find the total gross pay.
$400+$150=$550\$400 + \$150 = \$550
The total gross pay is the sum of the fixed retainer and any additional commission.

Key Concept

Calculating total gross pay by combining a fixed base salary with a percentage-based commission.
Question 42Question →

A manufacturing employee earns a base wage of $15.00\$15.00 per hour for a standard 40-hour workweek, with time-and-a-half pay for any additional hours worked. In addition to hourly wages, the employee earns a piece-rate bonus for every unit produced that exceeds a weekly quota of 100 units. Last week, the employee worked 48 hours, produced 180 units, and earned a total gross pay of $1,060.00\$1,060.00. What is the piece-rate bonus paid for each unit produced over the quota?

Show answer & explanation

Answer: $3.50\$3.50

Answer

The piece-rate bonus is $3.50\$3.50 per unit.
The correct piece-rate is found by first isolating the hourly wages. The employee earned $600.00\$600.00 for 40 regular hours and $180.00\$180.00 for 8 overtime hours (at $22.50\$22.50/hr), totaling $780.00\$780.00. Subtracting this from the $1,060.00\$1,060.00 gross pay leaves a $280.00\$280.00 bonus pool. Since the employee produced 80 units above the 100-unit quota, the rate per excess unit is $280.00÷80=$3.50\$280.00 \div 80 = \$3.50.

Step-by-Step Solution

1
Calculate the total hourly pay, including standard and overtime hours.
Regular pay: 40×$15.00=$600.0040 \times \$15.00 = \$600.00. Overtime pay: 8×($15.00×1.5)=8×$22.50=$180.008 \times (\$15.00 \times 1.5) = 8 \times \$22.50 = \$180.00. Total hourly pay = $780.00\$780.00.
You must isolate the hourly earnings from the total gross pay to determine how much money came from the piece-rate bonus.
2
Determine the total amount of the piece-rate bonus pool.
$1,060.00−$780.00=$280.00\$1,060.00 - \$780.00 = \$280.00
Subtracting the total hourly earnings from the total gross pay gives the exact amount earned purely from assembling extra units.
3
Determine the number of units eligible for the piece-rate bonus.
180−100=80180 - 100 = 80 units
The bonus is only paid for units produced that exceed the weekly quota of 100.
4
Calculate the bonus amount per excess unit.
$280.00÷80=$3.50\$280.00 \div 80 = \$3.50
Dividing the total bonus pool by the number of eligible units yields the individual piece-rate.

Key Concept

Calculating multi-component compensation by isolating variables (base pay, overtime, and piece-rate quotas).
Question 43Question →

An electronics refurbisher buys a lot of 55 broken laptops for $300\$300. The refurbisher spends an additional $150\$150 on replacement parts and $50\$50 on shipping. If the refurbisher wants to make a 40%40\% profit on the total investment, what must be the average selling price of each laptop?

Show answer & explanation

Answer: $140\$140

Answer

The correct selling price is $140\$140 per laptop.
The total investment is the sum of all costs: $300\$300 for the broken laptops, $150\$150 for replacement parts, and $50\$50 for shipping, which equals a total of $500\$500. To make a 40%40\% profit on the investment, the refurbisher needs to generate 140%140\% of the total cost in revenue (1.40×$500=$7001.40 \times \$500 = \$700). Dividing the $700\$700 total target revenue by the 55 laptops gives an average selling price of $140\$140 per laptop.

Step-by-Step Solution

1
Calculate the total cost (investment).
$300+$150+$50=$500\$300 + \$150 + \$50 = \$500
To find the total amount invested before calculating the desired profit.
2
Calculate the total revenue needed for a 40%40\% profit.
$500×1.40=$700\$500 \times 1.40 = \$700
To determine the total amount of money required to cover all costs and achieve the 40% profit margin.
3
Calculate the average selling price per laptop.
$700÷5=$140\$700 \div 5 = \$140
To distribute the total required revenue evenly across the 5 laptops.

Key Concept

Calculating net profit by determining total investment, applying a percentage markup, and finding unit price.
Estimated Time:1m 15s
Question 44Question →

A homeowner finances a new refrigerator using a $1,200\$1,200 store credit plan. The plan charges an annual simple interest rate of 5%5\%. If the homeowner pays off the balance in exactly 22 years without any prior payments, what is the total amount of interest paid, in dollars?

Show answer & explanation

Answer: 120

Answer

120
The total interest is found by multiplying the principal amount by the annual interest rate and the time in years. Using the formula I=P×R×TI = P \times R \times T, the calculation is 1200×0.05×21200 \times 0.05 \times 2, which equals $120.

Step-by-Step Solution

1
Identify the given values for principal, rate, and time.
Principal P=1200P = 1200, Rate R=5%=0.05R = 5\% = 0.05, Time T=2T = 2 years.
These are the necessary variables for the simple interest formula.
2
Apply the simple interest formula.
I=1200×0.05×2I = 1200 \times 0.05 \times 2
The formula for simple interest is I=P×R×TI = P \times R \times T.
3
Calculate the final product.
I=120I = 120
Multiplying the values determines the total interest paid over the 22-year period.

Key Concept

Calculating simple interest using the formula I=P×R×TI = P \times R \times T
Question 45Question →

A customer deposits $3,000\$3,000 into a savings account that pays an annual simple interest rate of 6%6\%. If no additional deposits or withdrawals are made, how much total interest will the account earn after 22 years?

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Answer: \$360

Answer

The account will earn $360\$360 in total interest.
The formula for simple interest is I=P×R×TI = P \times R \times T, where PP is the principal, RR is the annual interest rate as a decimal, and TT is the time in years. Substituting the given values: I=$3,000×0.06×2=$360I = \$3,000 \times 0.06 \times 2 = \$360.

Step-by-Step Solution

1
Identify the given values for principal, rate, and time.
P=$3,000P = \$3,000, R=6%=0.06R = 6\% = 0.06, T=2T = 2 years.
These are the necessary components for the simple interest formula.
2
Apply the simple interest formula I=P×R×TI = P \times R \times T.
I=$3,000×0.06×2I = \$3,000 \times 0.06 \times 2
This formula calculates the total interest earned over the given time period.
3
Multiply the values to find the total interest.
I=$360I = \$360
This provides the final amount of interest earned.

Key Concept

Simple Interest
Question 46Question →

A call center representative earns a base salary of $400\$400 per week, plus a $5\$5 bonus for every new customer account they open. If the representative opens 1515 new accounts in one week, what is their total gross pay for that week?

Fill in the blanks below

Total gross pay: $\$
Show answer & explanation

Answer

475
To find the total gross pay, you must first calculate the total bonus earned by multiplying the number of new accounts (1515) by the bonus per account ($5\$5). This gives a total bonus of $75\$75. You then add this bonus to the base weekly salary of $400\$400, which results in a total gross pay of $475\$475.

Step-by-Step Solution

1
Calculate the total bonus earned from opening new accounts.
$5×15=$75\$5 \times 15 = \$75
The representative earns a fixed bonus of $5\$5 for each of the 1515 accounts opened.
2
Add the total bonus to the weekly base salary to find the total gross pay.
$400+$75=$475\$400 + \$75 = \$475
Total gross pay is the sum of the guaranteed base salary and any additional bonuses earned during the week.

Key Concept

Calculating total gross pay by combining a fixed base salary with piecework or bonus earnings.
Question 47Question →

A restaurant manager wants to purchase a commercial refrigerator with a list price of $3,200\$3,200. Supplier A offers a single discount of 38%38\% off the list price. Supplier B offers a 25%25\% discount off the list price, followed by an additional 15%15\% discount applied to the newly reduced price.

How many dollars does the manager save by choosing the supplier with the lower final price instead of the other supplier?

Show answer & explanation

Answer: 56

Answer

56
Supplier A's final price is $1,984\$1,984 (after a 38%38\% reduction from $3,200\$3,200). Supplier B's final price is $2,040\$2,040 (after a 25%25\% reduction to $2,400\$2,400, followed by a 15%15\% reduction). Choosing Supplier A over Supplier B saves the manager $2,040−$1,984=$56\$2,040 - \$1,984 = \$56.

Step-by-Step Solution

1
Calculate Supplier A's final sale price.
$1,984\$1,984
Supplier A offers a single 38%38\% discount. 100%−38%=62%100\% - 38\% = 62\%. 0.62×$3,200=$1,9840.62 \times \$3,200 = \$1,984.
2
Calculate Supplier B's price after the initial discount.
$2,400\$2,400
Supplier B offers an initial 25%25\% discount. 100%−25%=75%100\% - 25\% = 75\%. 0.75×$3,200=$2,4000.75 \times \$3,200 = \$2,400.
3
Calculate Supplier B's final sale price.
$2,040\$2,040
Supplier B offers an additional 15%15\% off the reduced price. 100%−15%=85%100\% - 15\% = 85\%. 0.85×$2,400=$2,0400.85 \times \$2,400 = \$2,040.
4
Find the difference between the two final prices.
$56\$56
Subtracting Supplier A's price from Supplier B's price gives the total savings: $2,040−$1,984=$56\$2,040 - \$1,984 = \$56.

Key Concept

Calculating successive discounts and comparing final sale prices.
Question 48Question →

A commercial diver earns a base rate of $45.00\$45.00 per hour for the first 4040 hours worked in a week, time-and-a-half for the next 1010 hours (hours 4141 through 5050), and double time for any hours worked beyond 5050 hours. Additionally, the diver receives a $125\$125 hazard bonus for each dive exceeding a depth of 100100 feet. Last week, the diver logged a total of 5454 hours of work and completed 33 dives that exceeded 100100 feet in depth. Based on this information, calculate the diver's total gross pay for the week.

Fill in the blanks below

The diver's total gross pay for the week is $\$ .
Show answer & explanation

Answer

The total gross pay is $3,210\$3,210.
The correct answer accurately divides the 54 total hours into three distinct pay tiers: 40 hours at the base rate ($1,800\$1,800), 10 hours at 1.5x ($675\$675), and 4 hours at 2x ($360\$360). It then correctly adds the flat hazard bonus of $375\$375 (3×$1253 \times \$125) to reach the final gross pay of $3,210\$3,210.

Step-by-Step Solution

1
Calculate the standard pay for the first 40 hours.
$1,800\$1,800
$45.00×40=$1,800\$45.00 \times 40 = \$1,800
2
Calculate the time-and-a-half pay for the next 10 hours.
$675\$675
The time-and-a-half rate is $45.00×1.5=$67.50\$45.00 \times 1.5 = \$67.50. For 10 hours, this is $67.50×10=$675\$67.50 \times 10 = \$675.
3
Calculate the double time pay for the remaining hours over 50.
$360\$360
The diver worked 54 total hours, so 4 hours are paid at double time. The rate is $45.00×2=$90.00\$45.00 \times 2 = \$90.00. For 4 hours, this is $90.00×4=$360\$90.00 \times 4 = \$360.
4
Calculate the total hazard bonuses earned.
$375\$375
The diver completed 3 deep dives at $125\$125 each. 3×$125=$3753 \times \$125 = \$375.
5
Sum all compensation components to find the total gross pay.
$3,210\$3,210
$1,800+$675+$360+$375=$3,210\$1,800 + \$675 + \$360 + \$375 = \$3,210

Key Concept

Calculating multi-tiered compensation involving standard wages, multiple overtime multipliers, and piecework bonuses.
Estimated Time:2m 0s
Question 49Question →

A furniture store salesperson earns a weekly base salary of $500\$500, plus a 4%4\% commission on all sales. If the salesperson sells $3,000\$3,000 worth of furniture in a week, what is their total gross pay for that week?

Show answer & explanation

Answer: $620\$620

Answer

$620\$620
To find the total gross pay, you must first determine the commission earned by multiplying the total sales by the commission rate. 4%4\% of $3,000\$3,000 is $120\$120. Next, add this commission to the base salary. $500+$120=$620\$500 + \$120 = \$620. Therefore, the salesperson's total gross pay is $620\$620.

Step-by-Step Solution

1
Calculate the commission earned from the sales.
$3,000×0.04=$120\$3,000 \times 0.04 = \$120
The salesperson earns a 4% commission on their total sales volume.
2
Add the commission to the base salary to find the total gross pay.
$500+$120=$620\$500 + \$120 = \$620
Total gross pay is the sum of the fixed base salary and the variable commission.

Key Concept

Calculating total earnings by combining a fixed base salary with a percentage-based commission on sales.
Question 50Question →

A woodworker is purchasing a bulk supply of lumber with a regular total price of $800\$800. The supplier offers two different discount options for the purchase:

Option 1: A $150\$150 instant rebate on the regular price, followed by a 15%15\% discount on the remaining balance.
Option 2: A 25%25\% discount on the regular price, followed by an additional 5%5\% discount on the reduced price.

What is the positive difference in the final sale price between the two options?

Show answer & explanation

Answer: $17.50\$17.50

Answer

The correct difference between the two options is $17.50\$17.50.
Option 1 evaluates to $552.50\$552.50 by first subtracting the $150\$150 rebate and then taking 15%15\% off the remaining $650\$650. Option 2 evaluates to $570.00\$570.00 by first taking 25%25\% off the original $800\$800, yielding $600\$600, and then taking an additional 5%5\% off the $600\$600, which is $30\$30. The difference between $570.00\$570.00 and $552.50\$552.50 is $17.50\$17.50.

Step-by-Step Solution

1
Calculate the price for Option 1 after the instant rebate.
$800−$150=$650\$800 - \$150 = \$650
The rebate is a flat amount subtracted from the initial regular price before any percentage discounts are applied.
2
Calculate the final price for Option 1 after the 15% discount.
$650−($650×0.15)=$650−$97.50=$552.50\$650 - (\$650 \times 0.15) = \$650 - \$97.50 = \$552.50
The 15%15\% discount applies to the remaining balance of $650\$650.
3
Calculate the price for Option 2 after the initial 25% discount.
$800−($800×0.25)=$800−$200=$600\$800 - (\$800 \times 0.25) = \$800 - \$200 = \$600
The first discount is applied directly to the regular price.
4
Calculate the final price for Option 2 after the additional 5% discount.
$600−($600×0.05)=$600−$30=$570.00\$600 - (\$600 \times 0.05) = \$600 - \$30 = \$570.00
Successive discounts are applied to the newly reduced price, not the original price.
5
Calculate the positive difference between the two final prices.
$570.00−$552.50=$17.50\$570.00 - \$552.50 = \$17.50
Subtracting the smaller final price from the larger final price provides the difference.

Key Concept

Calculating successive discounts, rebates, and comparing multiple-step financial scenarios.
Question 51Question →

Read the scenario and fill in the missing numerical values for the discount and the sale price.

Fill in the blanks below

A hardware store is selling a power drill with a regular price of $120\$120. If the store is offering a 20%20\% discount on all power tools, calculate the savings and the new price.

Discount amount: $\$

Final sale price: $\$
Show answer & explanation

Answer

The discount amount is $24\$24, and the final sale price is $96\$96.
To find the discount amount, multiply the regular price ($120\$120) by the discount percentage (20%20\% or 0.200.20), which equals $24\$24. To find the final sale price, subtract the $24\$24 discount from the $120\$120 regular price, which equals $96\$96.

Step-by-Step Solution

1
Convert the discount percentage to a decimal.
20%=0.2020\% = 0.20
Percentages must be in decimal form to multiply them by dollar amounts.
2
Calculate the discount amount by multiplying the original price by the decimal discount rate.
$120×0.20=$24\$120 \times 0.20 = \$24
This determines the exact dollar amount that will be saved.
3
Subtract the discount amount from the original price to find the final sale price.
$120−$24=$96\$120 - \$24 = \$96
The final sale price is the original price minus the savings.

Key Concept

Calculating the dollar amount of a percentage discount and determining the final sale price.
Estimated Time:1m 0s
Question 52Question →

An individual borrows $4,000\$4,000 to purchase a used motorcycle. The loan has an annual simple interest rate of 7%7\%. If the loan is paid off in exactly 2424 months, how much total interest will the borrower pay?

Show answer & explanation

Answer: $560\$560

Answer

The total interest paid is $560\$560.
The correct answer accurately uses the simple interest formula I=P×R×TI = P \times R \times T. The principal (PP) is $4,000\$4,000, the rate (RR) is 0.070.07, and the time (TT) in years is 22 (since 2424 months equals 22 years). Multiplying these together yields $4,000×0.07×2=$560\$4,000 \times 0.07 \times 2 = \$560.

Step-by-Step Solution

1
Identify the principal amount (PP), annual interest rate (RR), and time (TT) given in the problem.
P=$4,000P = \$4,000, R=7%R = 7\%, and T=24T = 24 months.
These are the required variables for the simple interest formula.
2
Convert the interest rate from a percentage to a decimal.
7%=0.077\% = 0.07
Mathematical formulas require percentages to be in decimal form.
3
Convert the time duration from months to years to match the annual interest rate.
24 months÷12 months/year=2 years24 \text{ months} \div 12 \text{ months/year} = 2 \text{ years}.
The interest rate is annual, so the time must also be in years.
4
Apply the simple interest formula, I=P×R×TI = P \times R \times T.
I=$4,000×0.07×2=$560I = \$4,000 \times 0.07 \times 2 = \$560.
This calculates the total interest accrued over the 2-year period.

Key Concept

Simple Interest Calculation with Time Conversion
Question 53Question →

A marketing consultant earns a weekly base salary of $850\$850. She also earns a 4%4\% commission on any client contracts she secures beyond a weekly quota of $5,000\$5,000. If she secures $18,500\$18,500 in contracts this week, what are her total gross earnings?

Show answer & explanation

Answer: \$1,390

Answer

\$1,390
The correct answer is found by subtracting the $5,000\$5,000 quota from the total $18,500\$18,500 in contracts to find the commissionable amount ($13,500\$13,500). Then, calculating 4%4\% of that amount yields $540\$540 in commission. Finally, adding the $540\$540 commission to the $850\$850 base salary results in total gross earnings of $1,390\$1,390.

Step-by-Step Solution

1
Determine the amount of sales eligible for commission.
$18,500−$5,000=$13,500\$18,500 - \$5,000 = \$13,500
The consultant only earns commission on contracts beyond the $5,000\$5,000 quota.
2
Calculate the commission earned on the eligible sales.
0.04×$13,500=$5400.04 \times \$13,500 = \$540
The commission rate is 4%4\%, which is 0.040.04 as a decimal.
3
Add the commission to the base salary to find total gross earnings.
$850+$540=$1,390\$850 + \$540 = \$1,390
Total earnings are the sum of the fixed base salary and the variable commission.

Key Concept

Calculating gross pay involving a base salary and a tiered commission structure.
Estimated Time:1m 15s
Question 54Question →

An electronics salesperson earns a base weekly salary of $650\$650 plus a 6%6\% commission on their total sales. If they sell $4,500\$4,500 worth of electronics in one week, what is their total gross pay, in dollars, for that week?

Show answer & explanation

Answer: 920

Answer

920
The total gross pay is the sum of the base salary and the commission earned. The commission is 6%6\% of $4,500\$4,500, which is calculated as 0.06×4500=2700.06 \times 4500 = 270. Adding this to the base salary gives 650+270=920650 + 270 = 920.

Step-by-Step Solution

1
Calculate the commission earned from sales.
$270\$270
The commission is 6%6\% of the $4,500\$4,500 in total sales. Multiply 45004500 by 0.060.06 to find this amount.
2
Calculate the total gross pay.
$920\$920
Add the commission earned ($270\$270) to the base weekly salary ($650\$650) to determine the total earnings for the week.

Key Concept

Calculating total gross pay by combining a base salary with a percentage commission.
Question 55Question →

A craftsman purchases 6060 wooden boards at $3.00\$3.00 each to build custom storage chests. He spends an additional $40.00\$40.00 on hinges and pays a $20.00\$20.00 delivery fee for the materials. If he builds 1010 chests and sells them all for $30.00\$30.00 each, what is his profit percentage?

Show answer & explanation

Answer: 25%25\%

Answer

The profit percentage is 25%25\%.
The correct answer is found by first determining the total cost, which includes the materials and all overhead expenses ($180+$40+$20=$240\$180 + \$40 + \$20 = \$240). Next, find the total revenue ($30×10=$300\$30 \times 10 = \$300). The profit is the difference ($300−$240=$60\$300 - \$240 = \$60). Finally, divide the profit by the total cost to find the percentage: $60/$240=0.25\$60 / \$240 = 0.25, which is 25%25\%.

Step-by-Step Solution

1
Calculate the initial cost of the wooden boards.
60×$3.00=$180.0060 \times \$3.00 = \$180.00
To find the base material cost before adding overhead expenses.
2
Calculate the total cost (investment).
$180.00+$40.00 (hinges)+$20.00 (delivery)=$240.00\$180.00 + \$40.00 \text{ (hinges)} + \$20.00 \text{ (delivery)} = \$240.00
All overhead and preparation expenses must be included to find the true total cost.
3
Calculate the total revenue from selling the chests.
10×$30.00=$300.0010 \times \$30.00 = \$300.00
To determine the total amount earned from sales.
4
Calculate the profit amount.
$300.00−$240.00=$60.00\$300.00 - \$240.00 = \$60.00
Profit is the difference between total revenue and total cost.
5
Calculate the profit percentage.
(\$60.00 / \$240.00) \times 100 = 0.25 \times 100 = 25\%
Profit percentage is the profit amount divided by the total cost, expressed as a percentage.

Key Concept

Calculating percentage profit with multi-step overhead costs
Estimated Time:1m 15s
Question 56Question →

Read the problem carefully and fill in the blanks with the correct numerical values.

Fill in the blanks below

A military surplus store is selling tactical backpacks originally priced at 40.Theyarecurrentlyofferinga3040. They are currently offering a 30% discount on these items. The amount of the discount is and the new sale price is $.
Show answer & explanation

Answer

The discount amount is 12andthenewsalepriceis12 and the new sale price is 28.
To solve this problem, first determine the dollar value of the discount. Convert 30% to a decimal (0.30) and multiply it by the original price (40),whichresultsinadiscountamountof40), which results in a discount amount of 12. To find the new sale price, subtract the 12discountfromthe12 discount from the 40 original price, yielding a final sale price of $28.

Step-by-Step Solution

1
Calculate the discount amount in dollars.
40×0.30=40 \times 0.30 = 12
The discount is 30% of the original price, so multiplying the original price by the decimal equivalent of 30% yields the discount amount.
2
Calculate the new sale price.
40−40 - 12 = $28
The sale price is found by subtracting the discount amount from the original price.

Key Concept

Calculating simple discounts and final sale prices
Question 57Question →

A property leasing agent earns a fixed weekly base salary of $800\$800, plus a 5%5\% commission on the total dollar value of all leases signed that week. If the agent signed leases totaling $3,000\$3,000 last week, what was their total gross pay for the week?

Show answer & explanation

Answer: $950\$950

Answer

The agent's total gross pay is $950\$950.
The total gross pay is the sum of the base salary and the commission. The commission is calculated as 5%5\% of the $3,000\$3,000 lease value, which is $150\$150. Adding this to the $800\$800 base salary results in a total gross pay of $950\$950.

Step-by-Step Solution

1
Calculate the commission amount by finding 5%5\% of the total lease value.
0.05×$3,000=$1500.05 \times \$3,000 = \$150
The commission is earned on the total value of the leases signed.
2
Add the calculated commission to the fixed base salary to find the total gross pay.
$800+$150=$950\$800 + \$150 = \$950
Total pay is the sum of the guaranteed base salary and any earned commission.

Key Concept

Calculating total earnings by combining a fixed base salary with a percentage-based commission.
Question 58Question →

Calculate the unknown value in the following financial scenario.

Fill in the blanks below

A facilities manager is purchasing a bulk supply of LED lighting fixtures from a wholesale distributor. The distributor applies a 15%15\% volume discount to the regular total price. Because the manager pays the invoice within 10 days, an additional 5%5\% early-payment discount is applied to the already reduced price. If the final price of the fixtures before tax is $3,230\$3,230, the regular total price of the order was $\$$.
Show answer & explanation

Answer

$4,000
To find the original price after successive discounts, you must work backwards from the final price. First, divide the final price by the complement of the second discount (100%−5%=95%100\% - 5\% = 95\%, or 0.950.95) to find the intermediate price: $3,230÷0.95=$3,400\$3,230 \div 0.95 = \$3,400. Next, divide this intermediate price by the complement of the first discount (100%−15%=85%100\% - 15\% = 85\%, or 0.850.85) to find the regular total price: $3,400÷0.85=$4,000\$3,400 \div 0.85 = \$4,000.

Step-by-Step Solution

1
Calculate the intermediate price before the 5% early-payment discount.
$3,230÷0.95=$3,400\$3,230 \div 0.95 = \$3,400
The final price of $3,230\$3,230 represents 95%95\% (100%−5%100\% - 5\%) of the price after the initial volume discount.
2
Calculate the original regular total price before the 15% volume discount.
$3,400÷0.85=$4,000\$3,400 \div 0.85 = \$4,000
The intermediate price of $3,400\$3,400 represents 85%85\% (100%−15%100\% - 15\%) of the original regular total price.

Key Concept

Calculating original prices by reversing successive discounts using division.
Question 59Question →

A car wash attendant earns a base salary of $400\$400 per week, plus a 10%10\% commission on any detailing packages they sell. If the attendant sells $800\$800 worth of detailing packages in one week, what is their total gross pay for that week?

Fill in the blanks below

Total gross pay: $\$$
Show answer & explanation

Answer

480
The correct total gross pay is calculated by finding the commission (10%10\% of $800=$80\$800 = \$80) and adding it to the weekly base salary ($400\$400). The sum is $400+$80=$480\$400 + \$80 = \$480.

Step-by-Step Solution

1
Calculate the commission earned from the sale of detailing packages.
0.10×$800=$800.10 \times \$800 = \$80
The attendant earns a 10%10\% commission on the total value of detailing packages sold.
2
Add the commission to the base salary to find the total gross pay.
$400+$80=$480\$400 + \$80 = \$480
Total earnings equal the base salary plus any additional commission earned.

Key Concept

Calculating total gross pay using a base salary plus a percentage-based commission.
Question 60Question →

An outdoor gear shop is selling a camping tent with a regular price of $180.00\$180.00. During a weekend clearance event, the tent is discounted by 15%15\%. What is the sale price of the tent?

Show answer & explanation

Answer: $153.00\$153.00

Answer

$153.00\$153.00
The regular price of the tent is $180.00\$180.00. A 15%15\% discount means saving 15%15\% of the original price. Calculating 15%15\% of $180.00\$180.00 gives a $27.00\$27.00 discount. Subtracting this discount from the regular price ($180.00−$27.00\$180.00 - \$27.00) results in a final sale price of $153.00\$153.00.

Step-by-Step Solution

1
Calculate the discount amount by finding 15%15\% of $180.00\$180.00.
0.15×$180.00=$27.000.15 \times \$180.00 = \$27.00
To find the dollar amount of savings, multiply the original price by the discount percentage expressed as a decimal.
2
Subtract the discount amount from the regular price.
$180.00−$27.00=$153.00\$180.00 - \$27.00 = \$153.00
The final sale price is the original price reduced by the calculated discount amount.

Key Concept

Discounts and Sale Prices
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