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Financial Arithmetic

138 questions

All types138Multiple choice70Numeric32Matching5Ordering3Fill in the blank28
Question 121Question →

Read the scenario below and determine the missing values.

Fill in the blanks below

Marcus buys a new winter coat with a price tag of 80.00.Thestoreappliesa580.00. The store applies a 5% sales tax to all clothing purchases. The amount of sales tax added to his purchase is , which brings the total cost of the coat to $.
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Answer

The sales tax amount is 4.00andthetotalcostis4.00 and the total cost is 84.00.
First, the 5% tax on the 80.00coatiscalculatedbymultiplying80by0.05,yielding80.00 coat is calculated by multiplying 80 by 0.05, yielding 4.00 for the isolated tax amount. Then, this 4.00taxisaddedtotheinitial4.00 tax is added to the initial 80.00 price, resulting in a final total of $84.00.

Step-by-Step Solution

1
Calculate the amount of sales tax.
80.00×0.05=80.00 \times 0.05 = 4.00
To find the tax amount, convert the percentage (5%) to a decimal (0.05) and multiply it by the original price.
2
Calculate the final total cost.
80.00+80.00 + 4.00 = $84.00
The final total is the sum of the original price and the calculated sales tax.

Key Concept

Calculating sales tax amounts and finding the final total cost.
Question 122Question →

A corporate team of 88 employees goes out to dinner. The original food subtotal for the group is $400.00\$400.00. The team uses a coupon for 15%15\% off the food subtotal. The restaurant automatically adds an 18%18\% gratuity, which is calculated based on the original food subtotal before the discount. A 6%6\% sales tax is then applied only to the discounted food amount. The gratuity is not taxed. If the final total bill is split evenly among all 88 employees, how much does each employee pay?

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Answer: $54.05\$54.05

Answer

Each employee pays $54.05\$54.05.
The problem requires calculating three components based on specific amounts. First, the discounted subtotal is found by subtracting 15%15\% of $400\$400 ($60\$60) to get $340\$340. Second, the 6%6\% tax is applied to the $340\$340 discounted subtotal, adding $20.40\$20.40. Third, the 18%18\% gratuity is applied to the original $400\$400 subtotal, adding $72.00\$72.00. The total bill is $340+$20.40+$72.00=$432.40\$340 + \$20.40 + \$72.00 = \$432.40. Splitting this evenly among 88 employees gives $54.05\$54.05 per person.

Step-by-Step Solution

1
Calculate the discount and the discounted food subtotal.
Discount = 0.15×$400=$600.15 \times \$400 = \$60. Discounted subtotal = $400−$60=$340\$400 - \$60 = \$340.
The 15%15\% coupon is applied to the original subtotal to find the amount subject to sales tax.
2
Calculate the sales tax.
Tax = 0.06×$340=$20.400.06 \times \$340 = \$20.40.
The 6%6\% sales tax is applied only to the discounted food amount.
3
Calculate the gratuity.
Gratuity = 0.18×$400=$72.000.18 \times \$400 = \$72.00.
The gratuity must be calculated based on the original food subtotal ($400\$400), as explicitly stated in the problem.
4
Calculate the final total bill and split it evenly among the employees.
Total bill = $340+$20.40+$72.00=$432.40\$340 + \$20.40 + \$72.00 = \$432.40. Per employee = $432.40÷8=$54.05\$432.40 \div 8 = \$54.05.
The final bill is the sum of the discounted food, tax, and gratuity. Dividing by 88 gives the individual cost.

Key Concept

Multi-step financial arithmetic involving independent bases for taxes and tips, followed by proportional division.
Question 123Question →

An event planner organizes a retirement banquet. The standard cost for the food and beverage package is $500. The venue provides a 15% preferred client discount. A local sales tax of 8% is charged on the discounted price. In addition, an automatic gratuity of 20% is applied, which is also calculated based on the discounted price before tax. What is the total final cost of the banquet, in dollars?

Fill in the blanks below

Total final cost: $
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Answer

544
The final total is found by first applying the 15% discount to the original 500cost,yieldingadiscountedbaseof500 cost, yielding a discounted base of 425. Both the 8% sales tax (34)andthe2034) and the 20% gratuity ( 85) are calculated using this 425base.Addingthediscountedbaseprice,thetax,andthegratuitygivesafinaltotalof425 base. Adding the discounted base price, the tax, and the gratuity gives a final total of 544.

Step-by-Step Solution

1
Calculate the amount of the discount.
$75
The venue provides a 15% discount on the original $500 cost (0.15 × 500 = 75).
2
Determine the discounted price of the package.
$425
Subtract the discount amount from the original cost (500 - 75 = 425).
3
Calculate the sales tax.
$34
The 8% tax is charged on the $425 discounted price (0.08 × 425 = 34).
4
Calculate the gratuity.
$85
The 20% gratuity is also calculated based on the $425 discounted price (0.20 × 425 = 85).
5
Sum the components to find the total final cost.
$544
Add the discounted base price, the sales tax, and the gratuity together (425 + 34 + 85 = 544).

Key Concept

Calculating sequential percentages, including applying taxes and tips to a specific post-discount base amount.
Question 124Question →

A family books a guided kayak tour that originally costs $250.00\$250.00. They apply a promotional code that gives them a 20%20\% discount. After the discount is applied, an 8%8\% local booking tax is added. What is the final amount the family pays for the tour?

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Answer: $216.00\$216.00

Answer

$216.00\$216.00
The correct total is found by first reducing the original price by 20%20\% (a $50.00\$50.00 reduction, resulting in $200.00\$200.00). Then, an 8%8\% tax is calculated on this new balance ($200.00×0.08=$16.00\$200.00 \times 0.08 = \$16.00). Adding the tax to the discounted price yields $216.00\$216.00.

Step-by-Step Solution

1
Calculate the monetary value of the discount.
20%20\% of $250.00=0.20×250=$50.00\$250.00 = 0.20 \times 250 = \$50.00
The discount amount must be determined before calculating the new adjusted price.
2
Subtract the discount from the original price.
$250.00−$50.00=$200.00\$250.00 - \$50.00 = \$200.00
This finds the discounted subtotal, which is the amount subject to taxation.
3
Calculate the tax amount on the discounted price.
8%8\% of $200.00=0.08×200=$16.00\$200.00 = 0.08 \times 200 = \$16.00
Taxes are applied to the final selling price after discounts.
4
Add the tax to the discounted price to find the final total.
$200.00+$16.00=$216.00\$200.00 + \$16.00 = \$216.00
The customer pays the discounted price plus the applicable booking tax.

Key Concept

Calculating sequential percentages in financial transactions (discounts followed by taxes).
Question 125Question →

A customer brings their vehicle in for repairs. The mechanic's itemized bill lists $200.00\$200.00 for labor and $120.00\$120.00 for parts. The customer uses a promotional code that provides a 15%15\% discount on the labor cost. A 5%5\% sales tax is applied only to the cost of the parts. If the customer adds a 20%20\% tip calculated on the original pre-discount labor cost, what is the total amount the customer pays?

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Answer: $336.00\$336.00

Answer

The total amount the customer pays is $336.00\$336.00.
The total consists of four separate components: the discounted labor, the parts, the tax, and the tip. First, the discounted labor is $200−(0.15×$200)=$170\$200 - (0.15 \times \$200) = \$170. The parts remain at $120\$120. Second, the 5%5\% sales tax is applied only to the parts, resulting in an additional 0.05×$120=$60.05 \times \$120 = \$6. Finally, the 20%20\% tip is calculated strictly on the original $200\$200 labor cost, yielding $40\$40. Summing these amounts yields $170+$120+$6+$40=$336.00\$170 + \$120 + \$6 + \$40 = \$336.00.

Step-by-Step Solution

1
Calculate the discounted labor cost.
$170.00\$170.00
A 15%15\% discount on the $200.00\$200.00 labor cost is 0.15×200=300.15 \times 200 = 30. Subtracting this from the original cost gives $200−30=$170\$200 - 30 = \$170.
2
Calculate the sales tax on the parts.
$6.00\$6.00
The 5%5\% tax is only applied to the $120.00\$120.00 parts cost. 0.05×120=60.05 \times 120 = 6.
3
Calculate the tip based on the original labor cost.
$40.00\$40.00
The problem states the 20%20\% tip applies to the original pre-discount labor cost ($200.00\$200.00). 0.20×200=400.20 \times 200 = 40.
4
Sum all final costs to find the total amount paid.
$336.00\$336.00
Add the discounted labor, parts, tax on parts, and tip: $170+$120+$6+$40=$336.00\$170 + \$120 + \$6 + \$40 = \$336.00.

Key Concept

Calculating percentages on distinct bases in multi-step financial transactions.
Estimated Time:2m 0s
Question 126Question →

A customer pays for a car detailing service that costs $120.00\$120.00 before tax. If the local sales tax rate is 7%7\%, what is the total cost of the service including tax?

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Answer: $128.40\$128.40

Answer

The total cost of the service is $128.40\$128.40.
To find the total cost, first calculate the sales tax by converting 7%7\% to a decimal (0.070.07) and multiplying it by the original price of $120.00\$120.00, which equals $8.40\$8.40. Then, add this tax amount to the original price ($120.00+$8.40=$128.40\$120.00 + \$8.40 = \$128.40) to get the final total.

Step-by-Step Solution

1
Convert the sales tax percentage to a decimal.
7%=0.077\% = 0.07
Percentages must be expressed as decimals to perform mathematical operations.
2
Calculate the amount of sales tax.
$120.00×0.07=$8.40\$120.00 \times 0.07 = \$8.40
Multiplying the base price by the tax rate gives the total tax amount.
3
Add the tax amount to the original price to find the total cost.
$120.00+$8.40=$128.40\$120.00 + \$8.40 = \$128.40
The total cost includes the base price plus the applied tax.

Key Concept

Calculating sales tax and total cost
Question 127Question →

A customer orders groceries through a delivery service. The subtotal of the groceries is $50.00\$50.00. The service charges a 10%10\% delivery fee and an 8%8\% sales tax, both calculated on the grocery subtotal. The customer then adds a 20%20\% tip, which is calculated on the amount after the delivery fee and tax are applied. What is the total final cost to the customer?

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Answer: 70.8

Answer

70.80
The final cost is found by first determining the intermediate amount after the fee and tax are added to the subtotal. The delivery fee is $5.00\$5.00 (10%10\% of $50\$50) and the tax is $4.00\$4.00 (8%8\% of $50\$50), bringing the intermediate total to $59.00\$59.00. The 20%20\% tip is calculated sequentially on this $59.00\$59.00 amount, which equals $11.80\$11.80. Adding the tip to the intermediate total yields the final cost of $70.80\$70.80.

Step-by-Step Solution

1
Calculate the delivery fee based on the subtotal.
$50.00×0.10=$5.00\$50.00 \times 0.10 = \$5.00
The problem states the 10%10\% delivery fee is calculated on the grocery subtotal.
2
Calculate the sales tax based on the subtotal.
$50.00×0.08=$4.00\$50.00 \times 0.08 = \$4.00
The problem states the 8%8\% sales tax is also calculated on the grocery subtotal.
3
Calculate the intermediate total before the tip.
$50.00+$5.00+$4.00=$59.00\$50.00 + \$5.00 + \$4.00 = \$59.00
The tip is based on the amount after the delivery fee and tax are applied, so we must find this intermediate total.
4
Calculate the tip based on the intermediate total.
$59.00×0.20=$11.80\$59.00 \times 0.20 = \$11.80
The 20%20\% tip is applied to the intermediate total of $59.00\$59.00.
5
Calculate the final cost to the customer.
$59.00+$11.80=$70.80\$59.00 + \$11.80 = \$70.80
The final cost is the sum of the intermediate total and the tip.

Key Concept

Calculating sequential percentages for taxes, fees, and tips on a base amount.
Question 128Question →

A homeowner hires a landscaping service for an original quoted price of $450.00\$450.00. The company applies a 15%15\% promotional discount to this price. A local service tax of 8%8\% is then calculated based on the discounted amount. Finally, the homeowner adds a tip for the workers equal to 20%20\% of the original quoted price. What is the total amount, in dollars, that the homeowner pays?

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Answer: 503.1

Answer

503.10
The final amount is the sum of the discounted price, the tax calculated on the discounted price, and the tip calculated on the original price. Adding $382.50\$382.50, $30.60\$30.60, and $90.00\$90.00 yields a final total of $503.10\$503.10.

Step-by-Step Solution

1
Calculate the discount amount.
$67.50\$67.50
The discount is 15%15\% of the original $450.00\$450.00 price.
2
Determine the discounted subtotal.
$382.50\$382.50
Subtract the $67.50\$67.50 discount from the original $450.00\$450.00 price.
3
Calculate the service tax.
$30.60\$30.60
The 8%8\% tax is applied to the discounted subtotal of $382.50\$382.50.
4
Calculate the tip amount.
$90.00\$90.00
The 20%20\% tip is based on the original quoted price of $450.00\$450.00.
5
Calculate the final total cost.
$503.10\$503.10
Add the discounted subtotal ($382.50\$382.50), tax ($30.60\$30.60), and tip ($90.00\$90.00).

Key Concept

Calculating sequential percentage changes, including taxes on discounted amounts and tips on original amounts.
Question 129Question →

A social club reserves a private lounge for a holiday party. They receive a 25%25\% promotional discount on the standard food and beverage package price. A local hospitality tax of 6%6\% is applied to the discounted price, but the contract requires a mandatory 15%15\% gratuity calculated on the standard, pre-discount package price.

If the final bill paid by the club—consisting of the discounted package, the tax, and the gratuity—amounts to $378.00\$378.00, what was the standard package price before any discounts or fees?

Fill in the blanks below

The standard package price was $\.
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Answer

The standard package price was $400.
The total bill is the sum of the discounted price, the tax on the discounted price, and the tip on the original price. By setting the original price as PP, we can express the total cost algebraically: 0.75P0.75P (discounted price) +0.06(0.75P)+ 0.06(0.75P) (tax) +0.15P+ 0.15P (gratuity) =0.945P= 0.945P. Setting 0.945P=3780.945P = 378 and solving for PP yields exactly 400400.

Step-by-Step Solution

1
Let PP represent the standard package price. Express the discounted price in terms of PP.
Discounted Price = P−0.25P=0.75PP - 0.25P = 0.75P
The club receives a 25%25\% discount off the standard price.
2
Express the tax amount in terms of PP.
Tax = 0.06×0.75P=0.045P0.06 \times 0.75P = 0.045P
The problem states that the 6%6\% hospitality tax is applied to the discounted price.
3
Express the gratuity amount in terms of PP.
Gratuity = 0.15×P=0.15P0.15 \times P = 0.15P
The contract explicitly requires the 15%15\% tip to be calculated on the original, pre-discount package price.
4
Set up an equation for the final bill and solve for PP.
0.75P+0.045P+0.15P=378  ⟹  0.945P=378  ⟹  P=378÷0.945=4000.75P + 0.045P + 0.15P = 378 \implies 0.945P = 378 \implies P = 378 \div 0.945 = 400
The sum of the discounted package, the tax, and the gratuity equals the total final bill of $378.00\$378.00.

Key Concept

Solving for an original price when tax and tip are calculated using different base amounts (discounted vs. pre-discount).
Question 130Question →

An electronics restorer buys a bulk lot of 4040 tablets for $120\$120 each. The restorer spends an additional $1,200\$1,200 total for replacement parts to repair them. Unfortunately, 1010 of the tablets are too severely damaged to repair and must be discarded. If the restorer wants to make exactly a 25%25\% profit on the total investment, what must be the selling price for each of the remaining functional tablets?

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Answer: $250\$250

Answer

The restorer must sell each of the remaining tablets for $250\$250.
The total investment includes the bulk purchase price (40×$120=$4,80040 \times \$120 = \$4,800) plus the cost of replacement parts ($1,200\$1,200), which totals $6,000\$6,000. A 25%25\% profit on a $6,000\$6,000 investment requires $1,500\$1,500 in profit, meaning the total revenue must reach $7,500\$7,500. Because 1010 tablets were discarded, the restorer only has 3030 tablets left to sell. Dividing the target total revenue by the 3030 remaining tablets ($7,500÷30\$7,500 \div 30) gives a required selling price of $250\$250 for each functional tablet.

Step-by-Step Solution

1
Calculate the total cost of purchasing the tablets.
40 tablets×$120=$4,80040 \text{ tablets} \times \$120 = \$4,800
To determine the initial part of the investment.
2
Add the overhead costs to find the total investment.
$4,800+$1,200 (parts)=$6,000\$4,800 + \$1,200 \text{ (parts)} = \$6,000
Profit must be calculated based on the entire total investment, not just the purchase price.
3
Calculate the target total revenue required to achieve a 25%25\% profit.
$6,000×1.25=$7,500\$6,000 \times 1.25 = \$7,500
A 25%25\% profit means the revenue must be 125%125\% of the total investment.
4
Determine the number of functional tablets available to sell.
40−10=30 tablets40 - 10 = 30 \text{ tablets}
The discarded tablets generate no revenue, so the entire target revenue must be generated by the remaining inventory.
5
Calculate the required selling price per functional tablet.
$7,500÷30=$250\$7,500 \div 30 = \$250
Dividing the target total revenue by the number of sellable items gives the unit selling price.

Key Concept

Profit and Loss with Overhead and Inventory Shrinkage
Estimated Time:1m 30s
Question 131Question →

A couple hires a professional photographer for their wedding. The photographer's base package costs $1,200.00\$1,200.00. The contract includes a 9%9\% state service tax and a 15%15\% mandatory gratuity for the photography assistants. Both the tax and the gratuity are calculated based on the base package cost. What is the final total amount the couple will pay?

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Answer: $1,488.00\$1,488.00

Answer

The final total amount is $1,488.00\$1,488.00.
Both the tax and the gratuity are calculated independently on the base package cost. The tax is 9%9\% of $1,200.00\$1,200.00, yielding $108.00\$108.00. The gratuity is 15%15\% of $1,200.00\$1,200.00, yielding $180.00\$180.00. Adding these charges to the base cost gives $1,200.00+$108.00+$180.00=$1,488.00\$1,200.00 + \$108.00 + \$180.00 = \$1,488.00. Alternatively, combining the rates gives a total additional charge of 24%24\% (9%+15%9\% + 15\%). 24%24\% of $1,200.00\$1,200.00 is $288.00\$288.00, and $1,200.00+$288.00=$1,488.00\$1,200.00 + \$288.00 = \$1,488.00.

Step-by-Step Solution

1
Calculate the cost of the state service tax.
$1,200.00×0.09=$108.00\$1,200.00 \times 0.09 = \$108.00
The 9%9\% tax is applied directly to the base package cost.
2
Calculate the cost of the mandatory gratuity.
$1,200.00×0.15=$180.00\$1,200.00 \times 0.15 = \$180.00
The 15%15\% gratuity is also applied directly to the base package cost, as stated in the problem.
3
Add the tax and gratuity to the base cost to find the final total.
$1,200.00+$108.00+$180.00=$1,488.00\$1,200.00 + \$108.00 + \$180.00 = \$1,488.00
The final bill is the sum of the original price and all additional percentage-based fees.

Key Concept

Calculating and combining multiple percentages based on a single original amount.
Question 132Question →

A merchant buys a radio for 4040 dollars and sells it for 5050 dollars. What is the merchant's profit percentage on this item?

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Answer: 25%25\%

Answer

The correct answer is 25%25\%.
To find the profit percentage, first determine the total profit by subtracting the cost price (4040 dollars) from the selling price (5050 dollars), which gives a profit of 1010 dollars. Then, divide the profit by the original cost price (1040=0.25\frac{10}{40} = 0.25) and multiply by 100100 to get 25%25\%.

Step-by-Step Solution

1
Calculate the profit amount.
50−40=1050 - 40 = 10
Profit is defined as the difference between the selling price and the cost price.
2
Calculate the profit percentage.
1040×100=25%\frac{10}{40} \times 100 = 25\%
Profit percentage is the profit amount divided by the original cost price, expressed as a percentage.

Key Concept

Profit Percentage
Question 133Question →

An investor divides her 24,000savingsintotwodifferentaccounts.Sheplacesaportionintoahigh−yieldcertificateearning924,000 savings into two different accounts. She places a portion into a high-yield certificate earning 9% annual simple interest, and the remainder into a short-term bond earning 6% annual simple interest. After 18 months, the combined simple interest earned from both accounts is exactly 2,430. How much money was originally invested at the 9% rate?

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Answer: $6,000

Answer

The amount invested at the 9% rate is $6,000.
The correct answer is derived by modeling the split investment algebraically. By assigning xx to the 9% investment, the 6% investment becomes 24,000−x24,000 - x. Applying the formula I=PrtI = Prt with t=1.5t = 1.5 years to both parts yields 0.09(1.5)x+0.06(1.5)(24,000−x)=2,4300.09(1.5)x + 0.06(1.5)(24,000 - x) = 2,430. Simplifying this to 0.135x+2,160−0.09x=2,4300.135x + 2,160 - 0.09x = 2,430 leaves 0.045x=2700.045x = 270. Dividing 270 by 0.045 confirms that $6,000 was invested at 9%.

Step-by-Step Solution

1
Convert the investment duration from months to years.
18 months = 1.5 years.
The simple interest formula I=PrtI = Prt requires time tt to be expressed in years when dealing with annual interest rates.
2
Define variables for the two investment amounts.
Let xx be the amount invested at 9%. The remaining amount invested at 6% is (24,000−x)(24,000 - x).
This allows us to represent both unknown principals in terms of a single variable, making the equation solvable.
3
Set up the total interest equation using I=PrtI = Prt.
x(0.09)(1.5)+(24,000−x)(0.06)(1.5)=2,430x(0.09)(1.5) + (24,000 - x)(0.06)(1.5) = 2,430
The sum of the simple interest earned from the 9% account and the 6% account must equal the total interest of $2,430.
4
Distribute and simplify the terms in the equation.
0.135x+(24,000−x)(0.09)=2,430⇒0.135x+2,160−0.09x=2,4300.135x + (24,000 - x)(0.09) = 2,430 \Rightarrow 0.135x + 2,160 - 0.09x = 2,430
Multiplying the rate and time constants makes it easier to isolate xx.
5
Combine like terms and solve for xx.
0.045x=270⇒x=2700.045=6,0000.045x = 270 \Rightarrow x = \frac{270}{0.045} = 6,000
Isolating xx provides the original amount invested at the 9% rate.

Key Concept

Systems of Simple Interest
Estimated Time:3m 0s
Question 134Question →

Read the scenario and calculate the requested value. Enter only the exact numerical value in the blank.

Fill in the blanks below

An office manager orders a catered lunch for a team meeting. The food subtotal is $150.00\$150.00. The caterer adds a 6%6\% sales tax and an 18%18\% gratuity, both of which are calculated on the pre-tax subtotal. The final total cost of the lunch is $\$.
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Answer

The final total cost is $186.00\$186.00.
The correct total is obtained by recognizing that both the 6%6\% tax and the 18%18\% tip apply to the same base amount ($150.00\$150.00). Calculating 24%24\% of $150.00\$150.00 yields an additional $36.00\$36.00. Adding this to the original $150.00\$150.00 gives a final total of $186.00\$186.00.

Step-by-Step Solution

1
Calculate the combined percentage rate for both the sales tax and the gratuity.
6%+18%=24%6\% + 18\% = 24\%
Since both the tax and the tip are based on the same original subtotal, their percentages can be added together before calculating.
2
Convert the combined percentage to a decimal and multiply by the subtotal to find the total additional cost.
150.00×0.24=36.00150.00 \times 0.24 = 36.00
This represents the total amount of money added to the bill for the tax and gratuity.
3
Add the additional cost to the original subtotal to find the final total.
150.00+36.00=186.00150.00 + 36.00 = 186.00
The final cost is the sum of the food subtotal and all applied fees.

Key Concept

Calculating combined tax and tip on a fixed subtotal
Question 135Question →

A mechanic buys a new diagnostic tool for their shop. The tool is first marked down by 20%20\% for a storewide clearance. The mechanic then applies a special promotional code for an additional 15%15\% off the clearance price. Finally, a 6%6\% sales tax is applied to the discounted price.

If the total amount the mechanic paid, including the sales tax, was $864.96\$864.96, calculate the original price of the diagnostic tool before any discounts were applied.

Fill in the blanks below

The original price of the diagnostic tool was $\$$.
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Answer

The original price of the diagnostic tool was $1,200.
To find the original price, we must reverse each transaction step starting from the final price. First, we remove the 6%6\% sales tax by dividing $864.96\$864.96 by 1.061.06 to get $816.00\$816.00. Next, we reverse the 15%15\% discount by dividing $816.00\$816.00 by 0.850.85 (since the discounted price represents 85%85\% of the previous price), resulting in $960.00\$960.00. Finally, we reverse the 20%20\% clearance discount by dividing $960.00\$960.00 by 0.800.80, which yields the original price of $1,200.00\$1,200.00.

Step-by-Step Solution

1
Remove the 6%6\% sales tax from the final total to find the price of the tool after all discounts.
$864.96÷1.06=$816.00\$864.96 \div 1.06 = \$816.00
The final total represents 106%106\% of the discounted price. Dividing by 1.061.06 mathematically reverses the tax application.
2
Reverse the 15%15\% promotional discount to find the initial clearance price.
$816.00÷0.85=$960.00\$816.00 \div 0.85 = \$960.00
The price after the promo code was applied represents 85%85\% (100%−15%100\% - 15\%) of the clearance price. Dividing by 0.850.85 finds the value before this second discount.
3
Reverse the initial 20%20\% clearance markdown to determine the original price.
$960.00÷0.80=$1,200.00\$960.00 \div 0.80 = \$1,200.00
The clearance price represents 80%80\% (100%−20%100\% - 20\%) of the original price. Dividing by 0.800.80 finds the starting value.

Key Concept

Reversing successive percentage changes (chain discounts and taxes) using inverse operations to find an original value.
Question 136Question →

Match each retail and investment scenario to its correct net profit or net loss percentage. (Note: Calculate percentages based on total cost).

Click a left item, then click its matching right item

Items

Purchase a used motorcycle for $2,000\$2,000, spend $500\$500 on parts, and sell it for $3,000\$3,000.
Buy 100100 wholesale jackets at $15\$15 each plus $100\$100 total shipping. Sell 8080 jackets at $25\$25 each and discard the rest.
Acquire a commercial trailer for $15,000\$15,000 and invest $5,000\$5,000 in modifications. Sell the trailer later for $16,000\$16,000.
Purchase 2020 antique desks for $30\$30 each, spend $200\$200 on restoration supplies, then sell 1010 for $100\$100 each and 1010 for $20\$20 each.

Matches

Show answer & explanation

Answer

Motorcycle scenario matches 20%20\% net profit, jacket scenario matches 25%25\% net profit, trailer scenario matches 20%20\% net loss, and antique desk scenario matches 50%50\% net profit.
Each scenario requires calculating total cost, total revenue, and the net difference. Then, dividing that difference by the total cost yields the correct profit or loss percentage.

Step-by-Step Solution

1
Calculate the total cost for each scenario by adding the purchase price and any overhead or repair expenses.
Motorcycle cost = $2,500\$2,500; Jackets cost = $1,600\$1,600; Trailer cost = $20,000\$20,000; Desks cost = $800\$800.
Profit and loss are always calculated based on the total initial investment, not just the base price.
2
Calculate the total revenue for each scenario based on the items successfully sold.
Motorcycle revenue = $3,000\$3,000; Jackets revenue = $2,000\$2,000; Trailer revenue = $16,000\$16,000; Desks revenue = $1,200\$1,200.
Revenue must account for varied selling prices and discarded inventory.
3
Determine the dollar amount of profit or loss by subtracting the total cost from the revenue.
Motorcycle = +$500+\$500; Jackets = +$400+\$400; Trailer = −$4,000-\$4,000; Desks = +$400+\$400.
A positive value indicates a net profit, while a negative value indicates a net loss.
4
Calculate the percentage profit or loss by dividing the profit/loss by the total cost, then multiplying by 100%100\%.
Motorcycle = 20%20\% profit; Jackets = 25%25\% profit; Trailer = 20%20\% loss; Desks = 50%50\% profit.
This standardizes the dollar amounts into percentages to match the available options.

Key Concept

Calculating profit or loss percentages requires finding the total cost (including overhead) and total revenue, then dividing the net difference by the total cost.
Question 137Question →

A passenger takes a taxi ride that costs $30.00\$30.00 on the meter. The passenger wants to give the driver a 20%20\% tip. What is the total amount the passenger will pay in dollars?

Show answer & explanation

Answer: 36

Answer

36
The tip is calculated by converting 20%20\% to the decimal 0.200.20 and multiplying it by the $30.00\$30.00 meter cost, resulting in a $6.00\$6.00 tip. Adding this tip to the original $30.00\$30.00 cost gives a final total payment of $36.00\$36.00.

Step-by-Step Solution

1
Calculate the tip amount by finding 20%20\% of the meter cost.
$30.00×0.20=$6.00\$30.00 \times 0.20 = \$6.00
The tip is a percentage calculated based on the original cost of the service.
2
Add the tip amount to the original meter cost to find the total amount paid.
$30.00+$6.00=$36.00\$30.00 + \$6.00 = \$36.00
The total payment equals the original service cost plus the added tip.

Key Concept

Calculating a percentage of a base amount and adding it to find the total cost.
Question 138Question →

A retailer buys a wholesale lot of 100100 tablets for $4,000\$4,000. They pay an additional $1,000\$1,000 for shipping, software updates, and packaging before the tablets are ready for sale. The retailer sells 4040 of these tablets at a 10%10\% loss on their true unit cost. In order to achieve an overall profit of 20%20\% on the entire initial investment, what must be the selling price for each of the remaining tablets?

Show answer & explanation

Answer: $70\$70

Answer

The remaining tablets must be sold for $70\$70 each.
To achieve a 20% overall profit, the retailer must make a total of 6,000ona6,000 on a 5,000 total investment. Since the first 40 tablets were sold at a loss for 1,800total,theremaining1,800 total, the remaining 4,200 must be made up entirely by the remaining 60 tablets. Dividing 4,200by60yields4,200 by 60 yields 70 per tablet.

Step-by-Step Solution

1
Calculate the total investment and the target revenue.
Total Investment = $4,000\$4,000 + $1,000\$1,000 = $5,000\$5,000. Target Revenue = $5,000\$5,000 + (0.200.20 × $5,000\$5,000) = $6,000\$6,000.
To find how much money must be made in total, you must first account for all costs (purchase + overhead) and then add the desired 20% overall profit.
2
Determine the true unit cost per tablet.
Unit Cost = $5,000\$5,000 ÷ 100100 = $50\$50 per tablet.
The unit cost must reflect the total investment spread across all items, not just the original purchase price.
3
Calculate the revenue generated from the first 40 tablets.
Selling price = $50\$50 - (0.100.10 × $50\$50) = $45\$45. Revenue = 4040 × $45\$45 = $1,800\$1,800.
These tablets were sold at a 10% loss on their true unit cost.
4
Find the remaining revenue needed from the unsold tablets.
Remaining Revenue Needed = $6,000\$6,000 (Target) - $1,800\$1,800 (Collected) = $4,200\$4,200.
This is the exact dollar amount the remaining stock must generate to hit the overall profit goal.
5
Calculate the required selling price per remaining tablet.
Remaining tablets = 100100 - 4040 = 6060. Selling Price = $4,200\$4,200 ÷ 6060 = $70\$70.
Dividing the remaining revenue goal by the remaining inventory gives the required per-unit price.

Key Concept

Multi-stage Profit and Loss with Overhead Allocation
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