Financial Arithmetic

138 questions

Question 61Question →

A military mess hall requires exactly 500500 pounds of flour. Supplier A sells flour in 2525-pound bags for $14.00\$14.00 per bag. Supplier B sells the same flour in 4040-ounce boxes for $1.50\$1.50 per box. How much total money, in dollars, is saved by purchasing the entire 500500 pounds from the more cost-effective supplier instead of the less cost-effective one?

Show answer & explanation

Answer: 20

Answer

The savings amount to 20 dollars.
Supplier A's total cost for 500 pounds is 280(20bags×280 (20 bags × 14.00), and Supplier B's total cost is 300(200boxes×300 (200 boxes × 1.50). Purchasing from Supplier A saves $20.

Step-by-Step Solution

1
Convert the weight of Supplier B's boxes from ounces to pounds.
4040 ounces ÷16\div 16 ounces/pound = 2.52.5 pounds per box.
Measurements must be in the same unit (pounds) to accurately calculate the required number of packages and compare costs.
2
Determine the number of packages required from each supplier to get exactly 500 pounds.
Supplier A: 500÷25=20500 \div 25 = 20 bags. Supplier B: 500÷2.5=200500 \div 2.5 = 200 boxes.
This establishes the exact purchasing volume needed for the final cost calculation.
3
Calculate the total cost for each supplier.
Supplier A: 2020 bags ×$14.00\times \$14.00 = $280\$280. Supplier B: 200200 boxes ×$1.50\times \$1.50 = $300\$300.
Total cost is the package count multiplied by the price per package.
4
Calculate the difference between the two total costs.
$300−$280=$20\$300 - \$280 = \$20.
Subtracting the most cost-effective option from the alternative gives the total savings.

Key Concept

Calculating and comparing total costs across different measurement units by determining unit prices and required volumes.

Alternative Method

Instead of computing total costs, calculate the unit price per pound for both. Supplier A: $14.00÷25=$0.56\$14.00 \div 25 = \$0.56 per pound. Supplier B: 4040 oz is 2.52.5 lbs; $1.50÷2.5=$0.60\$1.50 \div 2.5 = \$0.60 per pound. The difference is $0.04\$0.04 per pound. Multiply this difference by the 500500 pounds needed: 500×$0.04=$20500 \times \$0.04 = \$20.
Estimated Time:2m 30s
Question 62Question →

A mechanic needs to buy a new set of socket wrenches. The regular price of the set is $150.00\$150.00. If the store is offering a 30%30\% discount on all tools, what is the final sale price of the socket wrench set in dollars?

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Answer: 105

Answer

The final sale price is $105.00\$105.00.
The correct answer is found by first determining the dollar value of the discount. A 30%30\% discount on $150.00\$150.00 is calculated as 150×0.30150 \times 0.30, which equals $45.00\$45.00. Subtracting this discount from the original price (150−45150 - 45) gives the final sale price of $105.00\$105.00.

Step-by-Step Solution

1
Calculate the discount amount.
$150.00×0.30=$45.00\$150.00 \times 0.30 = \$45.00
To find out how much money is being taken off the regular price.
2
Subtract the discount amount from the regular price.
$150.00−$45.00=$105.00\$150.00 - \$45.00 = \$105.00
To determine the final sale price after the discount is applied.

Key Concept

Calculating a single-step discount and determining the final sale price.
Question 63Question →

A boutique owner purchases 5050 plain canvas tote bags at a wholesale price of $8.00\$8.00 each. She pays a flat shipping fee of $100.00\$100.00 for the entire order and spends an additional $2.50\$2.50 per bag for custom screen printing. If she wants to make a 40%40\% profit on her total investment, what must be the selling price for a single custom tote bag?

Show answer & explanation

Answer: $17.50\$17.50

Answer

$17.50\$17.50
To find the selling price, the total cost per bag must first be established by combining the wholesale price, the per-bag shipping cost, and the printing fee ($8.00+$2.00+$2.50=$12.50\$8.00 + \$2.00 + \$2.50 = \$12.50). Finding 40%40\% of this comprehensive cost yields a $5.00\$5.00 profit, resulting in a final selling price of $17.50\$17.50.

Step-by-Step Solution

1
Calculate the total cost investment per individual tote bag, including all overhead expenses.
Wholesale: $8.00\$8.00. Shipping per bag: $100.00÷50=$2.00\$100.00 \div 50 = \$2.00. Printing: $2.50\$2.50. Total Cost = $8.00+$2.00+$2.50=$12.50\$8.00 + \$2.00 + \$2.50 = \$12.50.
Profit must be calculated on the total investment, which includes base cost, shipping, and modifications.
2
Determine the required profit amount per bag by calculating 40%40\% of the total cost.
40% of $12.50=0.40×12.50=$5.0040\% \text{ of } \$12.50 = 0.40 \times 12.50 = \$5.00.
The question asks for a 40%40\% profit margin on the total cost.
3
Add the calculated profit amount to the total cost to find the final selling price.
$12.50 (Total Cost)+$5.00 (Profit)=$17.50\$12.50 \text{ (Total Cost)} + \$5.00 \text{ (Profit)} = \$17.50.
The selling price is the sum of the total cost and the desired profit.

Key Concept

Calculating selling price based on total investment (cost plus overhead) and a desired profit percentage.
Estimated Time:1m 15s
Question 64Question →

A graphic designer is purchasing a new drawing tablet. The regular price of the tablet is $200.00\$200.00. If the electronics store is offering a 30%30\% discount on all tablets, what is the final sale price of the tablet?

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Answer: $140.00\$140.00

Answer

The final sale price of the drawing tablet is $140.00\$140.00.
To find the final sale price, first calculate the discount amount by multiplying the regular price by the discount percentage ($200.00×0.30=$60.00\$200.00 \times 0.30 = \$60.00). Then, subtract this discount amount from the regular price to find the total cost ($200.00−$60.00=$140.00\$200.00 - \$60.00 = \$140.00).

Step-by-Step Solution

1
Convert the discount percentage into a decimal.
30%=0.3030\% = 0.30
To calculate the discount amount, the percentage must be in decimal form.
2
Multiply the regular price by the decimal to find the discount amount.
$200.00×0.30=$60.00\$200.00 \times 0.30 = \$60.00
This determines exactly how much money will be taken off the regular price.
3
Subtract the discount amount from the regular price.
$200.00−$60.00=$140.00\$200.00 - \$60.00 = \$140.00
The final sale price is the original price minus the total savings.

Key Concept

Calculating a single-step percentage discount and subtracting it from the original price to find the final sale price.

Alternative Method

Instead of calculating the discount amount and subtracting, you can multiply the original price by the percentage you will actually pay. If the discount is 30%30\%, you are paying 100%−30%=70%100\% - 30\% = 70\% of the original price. Calculate 70%70\% of $200.00\$200.00: $200.00×0.70=$140.00\$200.00 \times 0.70 = \$140.00.
Estimated Time:45s
Question 65Question →

A supply clerk is comparing prices for standard issue notebooks. Vendor A sells a pack of 55 notebooks for 15.0015.00 dollars. Vendor B sells a bulk box of 2020 notebooks for 48.0048.00 dollars. What is the savings per notebook, in dollars, if the clerk chooses Vendor B instead of Vendor A?

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Answer: 0.6

Answer

0.60
The unit price is found by dividing the total cost by the quantity. Vendor A charges 15.00÷5=3.0015.00 \div 5 = 3.00 dollars per notebook. Vendor B charges 48.00÷20=2.4048.00 \div 20 = 2.40 dollars per notebook. The savings per notebook is the difference: 3.00−2.40=0.603.00 - 2.40 = 0.60 dollars.

Step-by-Step Solution

1
Calculate Vendor A's unit price
3.003.00 dollars per notebook
To find the cost of a single item in a package, divide the total price by the number of items (15.00÷515.00 \div 5).
2
Calculate Vendor B's unit price
2.402.40 dollars per notebook
Divide the bulk box total price by the number of notebooks it contains (48.00÷2048.00 \div 20).
3
Calculate the difference between the two unit prices
0.600.60 dollars
Subtracting Vendor B's unit price from Vendor A's unit price (3.00−2.403.00 - 2.40) gives the exact savings per notebook.

Key Concept

Unit price calculation and comparison
Question 66Question →

Read the scenario below and fill in the missing numerical values for the discount amount and percentage.

Fill in the blanks below

A gym owner is purchasing a set of free weights. The original price of the weights is $500\$500. During a seasonal clearance sale, the gym owner purchases the set for $400\$400.

Based on these prices, the dollar amount of the discount is $\$
and the discount percentage is %\%.
Show answer & explanation

Answer

The discount amount is $100 and the discount percentage is 20%.
The discount amount is the difference between the original price ($500\$500) and the sale price ($400\$400), which is $100\$100. The discount rate is the discount amount divided by the original price ($100/$500=0.20\$100 / \$500 = 0.20), which equals 20%20\%.

Step-by-Step Solution

1
Calculate the dollar amount of the discount.
Discount = $500\$500 - $400\$400 = $100\$100.
The discount amount is found by subtracting the sale price from the original price.
2
Calculate the discount percentage.
($100/$500)×100=0.20×100=20%(\$100 / \$500) \times 100 = 0.20 \times 100 = 20\%.
The discount rate is calculated by dividing the discount amount by the original price.

Key Concept

Calculating discount amounts and percentage rates based on original and sale prices.

Alternative Method

You can also determine the percentage the owner paid ($400/$500=0.80\$400 / \$500 = 0.80, or 80%80\%) and subtract that from 100%100\% to find the discount percentage (100%−80%=20%100\% - 80\% = 20\%).
Estimated Time:45s
Question 67Question →

A florist purchases 120120 wholesale roses for \50.00andpaysanadditional$30.00forcoldshipping.Upondelivery,50.00 and pays an additional \$30.00 for cold shipping. Upon delivery, 24 oftherosesarefoundtobedamagedandcannotbesold.Ifthefloristsellstheremainingrosesinbunchesofonedozen( of the roses are found to be damaged and cannot be sold. If the florist sells the remaining roses in bunches of one dozen ( 12$ roses) for \$12.50 per bunch, what is the florist's profit percentage on the total investment?

Show answer & explanation

Answer: 25%25\%

Answer

25%25\%
To find the profit percentage, first calculate the total investment: \50.00fortherosesplus$30.00forshippingequalsatotalcostof$80.00.Next,findthesellableinventorybysubtractingthe50.00 for the roses plus \$30.00 for shipping equals a total cost of \$80.00. Next, find the sellable inventory by subtracting the 24 damagedrosesfromtheoriginal damaged roses from the original 120 ,leaving, leaving 96 roses.Sincetheyaresoldbythedozen,divide roses. Since they are sold by the dozen, divide 96 by by 12 toget to get 8 bunches.Selling bunches. Selling 8 bunchesat$12.50eachgenerates$100.00intotalrevenue.Subtractthetotalcostfromtherevenuetofindtheprofit:$100.00−$80.00=$20.00.Finally,dividetheprofitbythetotalcosttofindthepercentage:$20.00÷$80.00=0.25 bunches at \$12.50 each generates \$100.00 in total revenue. Subtract the total cost from the revenue to find the profit: \$100.00 - \$80.00 = \$20.00. Finally, divide the profit by the total cost to find the percentage: \$20.00 \div \$80.00 = 0.25, which is 25%25\%.

Step-by-Step Solution

1
Calculate the total cost (investment).
\$50.00 + \$30.00 = \$80.00
Profit percentage must be calculated using the entire cost basis, including overhead like shipping.
2
Determine the number of sellable bunches.
120−24=96120 - 24 = 96 sellable roses. 96÷12=896 \div 12 = 8 bunches.
Damaged goods cannot be sold and must be subtracted from inventory before calculating revenue.
3
Calculate the total revenue.
$8×$12.50=$100.008 \times \$12.50 = \$100.00
Multiply the number of sellable units by the price per unit.
4
Calculate the profit and the profit percentage.
Profit = \$100.00 - \$80.00 = \$20.00. Percentage = (\$20.00 \div \$80.00) \times 100\% = 25\%.
Profit is revenue minus cost. Profit percentage is the profit divided by the total cost.

Key Concept

Calculating percentage profit requires finding the comprehensive total cost, determining actual total revenue (accounting for lost inventory), subtracting cost from revenue to find the profit amount, and then dividing that profit strictly by the total original cost.
Estimated Time:1m 30s
Question 68Question →

A cafeteria chef is purchasing black pepper. A 44-ounce jar of black pepper costs $8.00\$8.00. A 11-pound container of the same black pepper costs $16.00\$16.00. How much money is saved per ounce by purchasing the 11-pound container instead of the 44-ounce jar?

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Answer: \$1.00

Answer

The correct answer is $1.00\$1.00 saved per ounce.
The unit price of the 44-ounce jar is calculated by dividing its cost by its size: $8.00÷4 ounces=$2.00\$8.00 \div 4 \text{ ounces} = \$2.00 per ounce. Next, convert the 11-pound container to ounces, knowing that 1 pound=16 ounces1 \text{ pound} = 16 \text{ ounces}. The unit price of the 11-pound container is $16.00÷16 ounces=$1.00\$16.00 \div 16 \text{ ounces} = \$1.00 per ounce. The savings per ounce is found by subtracting the lower unit price from the higher unit price: $2.00−$1.00=$1.00\$2.00 - \$1.00 = \$1.00.

Step-by-Step Solution

1
Calculate the price per ounce for the 44-ounce jar.
$8.00÷4=$2.00\$8.00 \div 4 = \$2.00 per ounce
To compare prices, we need the unit price of the first option.
2
Convert the weight of the 11-pound container into ounces.
$1 \text{ pound} = 16 \text{ ounces}
Unit prices must be in the same measurement unit (ounces) to be compared.
3
Calculate the price per ounce for the 11-pound container.
$16.00÷16=$1.00\$16.00 \div 16 = \$1.00 per ounce
This establishes the unit price of the second option for comparison.
4
Subtract the lower unit price from the higher unit price to find the savings.
$2.00−$1.00=$1.00\$2.00 - \$1.00 = \$1.00 per ounce
The question asks for the exact amount of money saved per ounce.

Key Concept

Comparing unit prices requires converting different units of measurement into a common unit (like ounces) before dividing cost by quantity.
Estimated Time:45s
Question 69Question →

A catering manager is purchasing a commercial blender. The regular price of the blender is $400\$400. The store offers a 20%20\% discount. If a 5%5\% sales tax is applied to the discounted price, what is the final cost of the blender?

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Answer: $336\$336

Answer

The final cost is $336\$336.
To solve this problem, first determine the discount amount by multiplying the original price by the discount percentage: $400×0.20=$80\$400 \times 0.20 = \$80. Subtract this from the original price to find the discounted sale price: $400−$80=$320\$400 - \$80 = \$320. Next, calculate the 5%5\% sales tax on this new price: $320×0.05=$16\$320 \times 0.05 = \$16. Finally, add the tax to the sale price to find the total cost: $320+$16=$336\$320 + \$16 = \$336.

Step-by-Step Solution

1
Calculate the discount amount.
$400×0.20=$80\$400 \times 0.20 = \$80
To determine how much money is saved from the 20%20\% discount.
2
Calculate the sale price before tax.
$400−$80=$320\$400 - \$80 = \$320
To find the price that is actually subject to the sales tax.
3
Calculate the sales tax amount.
$320×0.05=$16\$320 \times 0.05 = \$16
To determine the additional amount owed for the 5%5\% tax on the sale price.
4
Calculate the final total cost.
$320+$16=$336\$320 + \$16 = \$336
To find the total amount the manager will pay at checkout.

Key Concept

Calculating final sale prices by applying percentage discounts followed by sales tax.

Alternative Method

You can calculate the final price in a single step using multipliers. A 20%20\% discount means you pay 80%80\% of the price (0.800.80). A 5%5\% tax means you pay 105%105\% of that amount (1.051.05). Chaining these gives: $400×0.80×1.05=$336\$400 \times 0.80 \times 1.05 = \$336.
Estimated Time:1m 0s
Question 70Question →

A quartermaster is evaluating different vendors to purchase AA batteries. Calculate the price per battery for each option and arrange the vendors in order from the lowest unit price to the highest unit price.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

Vendor Delta, Vendor Bravo, Vendor Alpha, Vendor Charlie
The correct sequence is found by evaluating the cost per single battery for each vendor. By dividing the total cost by the quantity provided, we find that Vendor Delta offers the lowest rate at $0.70\$0.70 per battery. Vendor Bravo follows at $0.80\$0.80 per battery, Vendor Alpha at $0.90\$0.90 per battery, and Vendor Charlie is the most expensive at $1.25\$1.25 per battery. Arranging these calculated unit prices from smallest to largest provides the correct order.

Step-by-Step Solution

1
Calculate the unit price for Vendor Alpha.
$9.00÷10=$0.90\$9.00 \div 10 = \$0.90 per battery.
To find the cost of a single battery, divide the total cost by the quantity.
2
Calculate the unit price for Vendor Bravo.
$9.60÷12=$0.80\$9.60 \div 12 = \$0.80 per battery.
To find the cost of a single battery, divide the total cost by the quantity.
3
Calculate the unit price for Vendor Charlie.
$2.50÷2=$1.25\$2.50 \div 2 = \$1.25 per battery.
To find the cost of a single battery, divide the total cost by the quantity.
4
Calculate the unit price for Vendor Delta.
$21.00÷30=$0.70\$21.00 \div 30 = \$0.70 per battery.
To find the cost of a single battery, divide the total cost by the quantity.
5
Order the calculated unit prices from lowest to highest.
$0.70\$0.70 (Delta) < $0.80\$0.80 (Bravo) < $0.90\$0.90 (Alpha) < $1.25\$1.25 (Charlie)
This establishes the correct sequence from the most cost-effective to the least cost-effective option.

Key Concept

Unit price is calculated by dividing the total price by the number of units. Comparing these prices reveals the lowest cost per item.
Question 71Question →

A photographer is buying a new camera bag. The original price of the bag is $80\$80. If the store is having a clearance sale and offers a 25%25\% discount, what is the final sale price of the camera bag in dollars?

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Answer: 60

Answer

The final sale price of the camera bag is $60\$60.
To find the final sale price, first calculate the discount amount by multiplying the original price ($80\$80) by the discount rate (25%25\% or 0.250.25), which equals $20\$20. Then, subtract this discount from the original price ($80−$20\$80 - \$20) to get the final sale price of $60\$60.

Step-by-Step Solution

1
Calculate the discount amount in dollars.
$20\$20
The discount is 25%25\% of the original price, so we multiply $80\$80 by 0.250.25.
2
Calculate the final sale price by subtracting the discount from the original price.
$60\$60
The final sale price is the original price minus the discount savings ($80−$20\$80 - \$20).

Key Concept

Calculating a single-step discount and final sale price.
Question 72Question →

An entrepreneur purchases 55 used electric scooters for $120\$120 each. She pays an additional flat fee of $150\$150 to replace the batteries for the entire batch. If she sells all 55 scooters for $210\$210 each, what is her overall profit percentage on this investment?

Show answer & explanation

Answer: 40

Answer

40
The correct answer is found by first calculating the total investment, which includes both the purchase price of the scooters (600)andthebatteryreplacementcosts(600) and the battery replacement costs ( 150), yielding a total cost basis of 750.Thetotalrevenuefromsalesis750. The total revenue from sales is 1,050. Subtracting the total cost from the revenue gives a net profit of 300.Finally,dividingthe300. Finally, dividing the 300 profit by the $750 total investment yields a profit percentage of 40%.

Step-by-Step Solution

1
Calculate the total cost of purchasing the used scooters.
5×$120=$6005 \times \$120 = \$600
This establishes the initial base cost before overhead.
2
Calculate the total investment by adding the battery replacement cost.
$600+$150=$750\$600 + \$150 = \$750
Profit must be calculated using the total cost basis, including all overhead expenses.
3
Calculate the total revenue from selling the scooters.
5×$210=$1,0505 \times \$210 = \$1,050
Total revenue is needed to find the net profit.
4
Determine the net profit.
$1,050−$750=$300\$1,050 - \$750 = \$300
Net profit is total revenue minus total investment.
5
Calculate the profit percentage.
300750×100=40%\frac{300}{750} \times 100 = 40\%
Profit percentage is the net profit divided by the total investment (cost basis), expressed as a percentage.

Key Concept

Calculating profit percentage by factoring in both unit costs and multi-step overhead expenses.
Estimated Time:1m 0s
Question 73Question →

Sarah works as a wholesale medical supplier. She is compensated with a fixed weekly base pay of $750\$750. In addition to her base pay, she receives an 8%8\% commission on the portion of her weekly sales that exceeds a $5,000\$5,000 quota. If her total sales for the week amount to $12,500\$12,500, what is her total gross earnings for the week?

Show answer & explanation

Answer: $1,350\$1,350

Answer

$1,350\$1,350
To find the total gross earnings, you must first identify the sales amount subject to commission by subtracting the quota from the total sales ($12,500−$5,000=$7,500\$12,500 - \$5,000 = \$7,500). Next, find the 8%8\% commission on that amount (0.08×7,500=$6000.08 \times 7,500 = \$600). Finally, add the commission to the fixed base pay ($750+$600=$1,350\$750 + \$600 = \$1,350).

Step-by-Step Solution

1
Determine the amount of sales eligible for commission.
$12,500−$5,000=$7,500\$12,500 - \$5,000 = \$7,500
The commission is only applied to the portion of sales that exceeds the $5,000 quota.
2
Calculate the commission earned.
8% of $7,500=0.08×7,500=$6008\% \text{ of } \$7,500 = 0.08 \times 7,500 = \$600
Multiply the commissionable sales by the commission rate (expressed as a decimal) to find the extra earnings.
3
Calculate the total gross earnings.
$750+$600=$1,350\$750 + \$600 = \$1,350
Add the base pay to the earned commission to find the total gross pay for the week.

Key Concept

Calculating gross pay involving a base salary and a commission with a sales quota.
Question 74Question →

A base recreation center needs to purchase tennis balls for an upcoming tournament. A single can of tennis balls costs $4.50\$4.50. A case containing 1010 cans costs $40.00\$40.00. How much money is saved per can by purchasing the case instead of individual cans?

Show answer & explanation

Answer: $0.50\$0.50

Answer

$0.50\$0.50
Purchasing the case means each can costs $40.00\$40.00 divided by 1010, which is $4.00\$4.00 per can. Subtracting this bulk unit price from the individual price of $4.50\$4.50 gives a savings of $0.50\$0.50 per can.

Step-by-Step Solution

1
Calculate the unit price of a single can when bought by the case.
$40.00÷10=$4.00\$40.00 \div 10 = \$4.00 per can
To compare prices on equal terms, you must find the cost of one unit for the bulk option.
2
Calculate the difference between the individual can price and the bulk unit price.
$4.50−$4.00=$0.50\$4.50 - \$4.00 = \$0.50
Subtracting the lower unit price from the higher individual price reveals the exact savings per can.

Key Concept

Comparing the unit rate of a bulk purchase to an individual item price to determine savings.
Estimated Time:45s
Question 75Question →

A restaurant owner is purchasing bulk cleaning supplies. The regular price for the order is $250\$250. If the wholesale supplier offers a 10%10\% discount on the entire order, what is the final sale price?

Show answer & explanation

Answer: $225\$225

Answer

The final sale price is $225\$225.
To find the final sale price, first calculate the discount amount by finding 10%10\% of $250\$250, which is $25\$25. Then, subtract the discount amount from the original price: $250−$25=$225\$250 - \$25 = \$225.

Step-by-Step Solution

1
Calculate the discount amount by finding 10%10\% of the regular price.
0.10×250=250.10 \times 250 = 25
The discount amount must be determined before it can be subtracted from the total.
2
Subtract the discount amount from the regular price.
250−25=225250 - 25 = 225
The final sale price is the original price minus the discount savings.

Key Concept

Discounts and Sale Prices
Question 76Question →

Read the scenario below and determine the technician's total gross earnings for the week.

Fill in the blanks below

An industrial equipment technician is paid an hourly rate of $28.00\$28.00 for a standard 4040-hour workweek. Any additional hours are compensated at time-and-a-half. Last week, the technician worked a total of 4747 hours and also received a flat $75.00\$75.00 emergency call-out fee.

The technician's total gross earnings for that week were $\$
$.
Show answer & explanation

Answer

The technician's total gross earnings for the week are $1,489.
The correct total is calculated by evaluating each component of the technician's compensation separately. The standard pay for the first 40 hours is 1,120.The7overtimehoursarepaidatatime−and−a−halfrateof1,120. The 7 overtime hours are paid at a time-and-a-half rate of 42 per hour, contributing 294.Addingthestandardpay,theovertimepay,andthe294. Adding the standard pay, the overtime pay, and the 75 flat fee results in a total gross earnings of $1,489.

Step-by-Step Solution

1
Calculate the pay for the standard 40-hour workweek.
40 hours×$28.00/hour=$1,120.0040 \text{ hours} \times \$28.00/\text{hour} = \$1,120.00
The standard hourly wage applies only to the first 40 hours worked.
2
Determine the overtime pay rate and the number of overtime hours.
Overtime rate = $28.00×1.5=$42.00\$28.00 \times 1.5 = \$42.00 per hour. Overtime hours = 47−40=747 - 40 = 7 hours.
Any hours worked beyond the standard 40 hours are paid at the time-and-a-half rate.
3
Calculate the total overtime pay.
7 hours×$42.00/hour=$294.007 \text{ hours} \times \$42.00/\text{hour} = \$294.00
This represents the earnings from the additional 7 hours worked.
4
Sum the standard pay, overtime pay, and the flat emergency fee to find the total gross earnings.
$1,120.00+$294.00+$75.00=$1,489.00\$1,120.00 + \$294.00 + \$75.00 = \$1,489.00
Total gross earnings include all forms of compensation before taxes and deductions.

Key Concept

Calculating total gross pay involving a standard hourly wage, time-and-a-half overtime pay, and additional flat fees.
Question 77Question →

A freight broker earns a weekly base salary of $600\$600. They also earn a 3%3\% commission on their first $10,000\$10,000 in freight sales for the week, and a 5%5\% commission on any sales exceeding $10,000\$10,000. If the broker secures $24,000\$24,000 in freight sales this week, what are their total gross earnings for the week in dollars?

Show answer & explanation

Answer: 1600

Answer

1600
The total earnings consist of three parts: the fixed base salary (600),the3600), the 3% commission on the first 10,000 of sales (300),andthe5300), and the 5% commission on the remaining 14,000 of sales (700).Addingtheseamountstogether(700). Adding these amounts together ( 600 + 300+300 + 700) results in total gross earnings of $1,600.

Step-by-Step Solution

1
Calculate the commission earned on the first $10,000 of sales.
$300
The broker earns 3% on the first 10,000.10,000. 10,000 \times 0.03 = $300.
2
Calculate the remaining sales volume above the $10,000 threshold.
$14,000
Total sales were 24,000.Theamountover24,000. The amount over 10,000 is 24,000−24,000 - 10,000 = $14,000.
3
Calculate the commission earned on the remaining sales.
$700
The broker earns 5% on sales exceeding 10,000.10,000. 14,000 \times 0.05 = $700.
4
Calculate total gross earnings.
$1,600
Add the base salary, first-tier commission, and second-tier commission: 600+600 + 300 + 700=700 = 1,600.

Key Concept

Calculating total gross earnings involving a base salary and a tiered commission structure.
Estimated Time:1m 30s
Question 78Question →

A custom cabinetry builder is paid an hourly wage of $24\$24 for a standard 4040-hour workweek. For any hours worked beyond 4040 in a single week, they receive "time-and-a-half" overtime pay. Last week, the builder worked a total of 5252 hours and received an additional $150\$150 material handling bonus. What were the builder's total gross earnings for the week?

Show answer & explanation

Answer: $1,542\$1,542

Answer

The total gross earnings are $1,542\$1,542.
The correct answer accurately separates the total hours into regular and overtime components, applies the respective rates to each portion, and includes the fixed material handling bonus to find the total gross earnings.

Step-by-Step Solution

1
Calculate the base pay for the standard workweek.
40 hours×$24/hour=$96040 \text{ hours} \times \$24/\text{hour} = \$960
The standard hourly rate only applies to the first 40 hours worked in the week.
2
Determine the number of overtime hours and the overtime pay rate.
52−40=12 overtime hours52 - 40 = 12 \text{ overtime hours}. The overtime rate is $24×1.5=$36/hour\$24 \times 1.5 = \$36/\text{hour}.
Overtime is paid at time-and-a-half for any hours beyond the standard 40.
3
Calculate the total overtime pay.
12 hours×$36/hour=$43212 \text{ hours} \times \$36/\text{hour} = \$432
This accounts for the compensation earned during the extra hours.
4
Sum all earnings to find the total gross pay.
$960 (base)+$432 (overtime)+$150 (bonus)=$1,542\$960 \text{ (base)} + \$432 \text{ (overtime)} + \$150 \text{ (bonus)} = \$1,542
Total gross earnings must include regular pay, overtime pay, and any additional bonuses.

Key Concept

Wages, Salaries, and Commissions
Question 79Question →

A machinist earns a regular hourly rate of $26.00\$26.00 for a standard 4040-hour workweek. Any hours worked over 4040 in a single week are paid at a time-and-a-half overtime rate. Additionally, working the night shift adds a flat $3.50\$3.50 per hour differential to their base rate before the overtime multiplier is applied. If the machinist worked 4646 hours last week, and all of those hours were on the night shift, what was their total gross pay in dollars?

Show answer & explanation

Answer: 1445.5

Answer

1445.50
The total gross pay is calculated by first establishing the adjusted base rate for the night shift, which is the regular rate plus the differential: $26.00+$3.50=$29.50\$26.00 + \$3.50 = \$29.50. The machinist worked 4040 regular hours at this rate, earning 40×$29.50=$1,180.0040 \times \$29.50 = \$1,180.00. The 66 remaining hours are overtime, paid at 1.51.5 times the adjusted rate: $29.50×1.5=$44.25\$29.50 \times 1.5 = \$44.25. Multiplying this by the 66 overtime hours gives 6×$44.25=$265.506 \times \$44.25 = \$265.50. Adding the regular pay and overtime pay results in a total gross pay of $1,180.00+$265.50=$1,445.50\$1,180.00 + \$265.50 = \$1,445.50.

Step-by-Step Solution

1
Calculate the adjusted base hourly rate.
$26.00+$3.50=$29.50\$26.00 + \$3.50 = \$29.50 per hour
The night shift differential is added to the standard base rate before any other multipliers are applied.
2
Calculate the regular pay for the first 40 hours.
40×$29.50=$1,180.0040 \times \$29.50 = \$1,180.00
The standard workweek is 40 hours, which is paid at the regular adjusted rate.
3
Calculate the overtime hourly rate.
$29.50×1.5=$44.25\$29.50 \times 1.5 = \$44.25 per hour
Overtime is paid at time-and-a-half (1.5 times the regular rate), applying to the adjusted base rate.
4
Calculate the pay for the overtime hours.
6×$44.25=$265.506 \times \$44.25 = \$265.50
The machinist worked 46 hours total, so 6 of those hours are considered overtime.
5
Calculate the total gross pay.
$1,180.00+$265.50=$1,445.50\$1,180.00 + \$265.50 = \$1,445.50
Total gross pay is the sum of the regular shift pay and the overtime pay.

Key Concept

Calculating gross pay involving base rate adjustments, shift differentials, and overtime multipliers.
Question 80Question →

A retail boutique manager receives a fixed monthly salary of $3,200\$3,200. In addition to this base pay, she earns a 3%3\% commission on her own personal sales and a 0.5%0.5\% override commission on the sales generated by her staff. Last month, her personal sales totaled $14,000\$14,000, and her staff's sales totaled $38,000\$38,000. What was the manager's total gross income for the month?

Show answer & explanation

Answer: $3,810

Answer

$3,810\$3,810
To find the total gross income, calculate the separate commissions and add them to the base salary. The personal commission is 3%3\% of $14,000\$14,000 (which is $420\$420) and the staff commission is 0.5%0.5\% of $38,000\$38,000 (which is $190\$190). Adding these variable amounts to the fixed $3,200\$3,200 base salary yields a total of $3,810\$3,810.

Step-by-Step Solution

1
Calculate the commission earned from personal sales.
$14,000×0.03=$420\$14,000 \times 0.03 = \$420
The manager earns a 3% commission on her $14,000 of personal sales.
2
Calculate the override commission earned from staff sales.
$38,000×0.005=$190\$38,000 \times 0.005 = \$190
The manager earns a 0.5% commission on the $38,000 sold by her staff. Note that 0.5% is 0.005 in decimal form.
3
Add the base salary and both commission amounts to find the total gross income.
$3,200+$420+$190=$3,810\$3,200 + \$420 + \$190 = \$3,810
Gross income is the sum of all fixed pay and variable earnings before taxes.

Key Concept

Calculating Gross Pay with Base Salary and Multiple Commission Rates
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