Examkin

Discounts and Sale Prices

29 questions

All types29Multiple choice13Numeric7Fill in the blank9
Question 1Question →

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

Fill in the blanks below

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

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

Answer

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

Step-by-Step Solution

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

Key Concept

Successive Discounts
Question 2Question →

A contractor purchases a bulk order of electrical wiring from a wholesale supply store. The store offers a 25%25\% discount on all orders over $500\$500. Because the contractor is a loyal member, they receive an additional 10%10\% off the already discounted price. After both discounts are applied, an 8%8\% sales tax is added. If the original price of the electrical wiring order was $800\$800, what is the final total amount the contractor pays?

Show answer & explanation

Answer: $583.20\$583.20

Answer

The final total amount the contractor pays is $583.20\$583.20.
The final amount must be calculated sequentially. First, apply the 25%25\% discount to $800\$800, resulting in $600\$600. Then, apply the 10%10\% loyal member discount to $600\$600, resulting in $540\$540. Finally, calculate 8%8\% sales tax on the $540\$540 final price ($540×0.08=$43.20\$540 \times 0.08 = \$43.20) and add it to the price to get $\$583.20.

Step-by-Step Solution

1
Calculate the first 25%25\% discount on the original $800\$800 price.
$800×0.25=$200\$800 \times 0.25 = \$200 discount. The new price is $800−$200=$600\$800 - \$200 = \$600.
The first discount is applied to the original wholesale price.
2
Calculate the second 10%10\% loyal member discount on the new price of $600\$600.
$600×0.10=$60\$600 \times 0.10 = \$60 discount. The new price is $600−$60=$540\$600 - \$60 = \$540.
Successive discounts are always applied to the previously discounted amount, not the original price.
3
Calculate the 8%8\% sales tax on the final discounted price and add it to the total.
$540×0.08=$43.20\$540 \times 0.08 = \$43.20 tax. The final total is $540+$43.20=$583.20\$540 + \$43.20 = \$583.20.
Sales tax is applied to the final amount after all discounts have been deducted.

Key Concept

Calculating successive discounts and applying sales tax to the final discounted price.
Question 3Question →

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 4Question →

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 5Question →

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 6Question →

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 $.
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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 7Question →

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 $\$$.
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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 8Question →

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
Question 9Question →

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?

Show answer & explanation

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 10Question →

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 11Question →

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 12Question →

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?

Show answer & explanation

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 13Question →

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?

Show answer & explanation

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 14Question →

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 15Question →

Determine the total amount saved and the final pre-tax price for the successive discounts described below.

Fill in the blanks below

An auto parts store lists a set of all-terrain tires for a regular price of $800\$800. During a holiday event, the tires are marked down by 15%15\%. A customer applies a military discount that takes an additional 10%10\% off the already reduced sale price. The customer saves a total of $\$fromtheregularprice,resultinginafinalpre−taxpriceof from the regular price, resulting in a final pre-tax price of \$$.
Show answer & explanation

Answer

The total savings is $188\$188, and the final price is $612\$612.
To find successive discounts, each percentage must be applied to the current reduced price. First, a 15%15\% discount on $800\$800 reduces the price by $120\$120, making it $680\$680. Then, a 10%10\% discount is applied to the $680\$680 sale price, which reduces it by another $68\$68. The final price is $680−$68=$612\$680 - \$68 = \$612. The total amount saved is the sum of both discounts, $120+$68=$188\$120 + \$68 = \$188.

Step-by-Step Solution

1
Calculate the first discount amount.
$800×0.15=$120\$800 \times 0.15 = \$120
Find the dollar value of the initial 15%15\% holiday mark-down.
2
Calculate the intermediate sale price.
$800−$120=$680\$800 - \$120 = \$680
Subtract the first discount from the regular price to find the new base price for the second discount.
3
Calculate the second discount amount.
$680×0.10=$68\$680 \times 0.10 = \$68
Apply the 10%10\% military discount to the intermediate sale price, not the original price.
4
Determine the total savings and final price.
Total savings: $120+$68=$188\$120 + \$68 = \$188. Final price: $800−$188=$612\$800 - \$188 = \$612.
Combine both discount amounts to find the total saved, and subtract from the original price to find the final price.

Key Concept

Calculating successive discounts requires applying the second percentage to the newly reduced price, rather than adding the percentages together.
Estimated Time:1m 30s
Question 16Question →

A customer is purchasing a winter coat that has an original price of $140\$140. The store offers a 25%25\% discount on the coat. After the discount is applied, a 6%6\% sales tax is added to the purchase. What is the final total cost of the winter coat?

Show answer & explanation

Answer: $111.30\$111.30

Answer

The final total cost of the winter coat is $111.30\$111.30.
The correct answer accurately calculates the discounted price first ($105\$105), and then correctly applies the 6%6\% sales tax to that new, lower amount ($105×1.06=$111.30\$105 \times 1.06 = \$111.30).

Step-by-Step Solution

1
Calculate the discount amount.
$140×0.25=$35\$140 \times 0.25 = \$35
To find how much money will be taken off the original price, multiply the original price by the discount percentage.
2
Determine the discounted sale price.
$140−$35=$105\$140 - \$35 = \$105
Subtract the discount amount from the original price to find the price before tax.
3
Calculate the sales tax on the discounted price.
$105×0.06=$6.30\$105 \times 0.06 = \$6.30
Sales tax is applied only to the final sale price, not the original sticker price.
4
Calculate the final total cost.
$105+$6.30=$111.30\$105 + \$6.30 = \$111.30
Add the sales tax amount to the discounted sale price to find the final amount paid at the register.

Key Concept

Discounts and Sale Prices
Question 17Question →

An electronics store is liquidating its marine equipment inventory. A high-frequency boat radar system is marked down by 20%20\% from its original price. During a special weekend clearance event, an additional 10%10\% is taken off the already discounted price. If the final sale price of the radar system is $360\$360, what was the original price of the system in dollars?

Show answer & explanation

Answer: 500

Answer

The original price of the radar system was $500.
The correct answer is found by setting up an equation with successive multipliers for each discount phase: x×0.80×0.90=360x \times 0.80 \times 0.90 = 360. Simplifying the left side yields 0.72x=3600.72x = 360, and dividing by 0.720.72 correctly identifies the original price as $500.

Step-by-Step Solution

1
Set up an expression for the price after the first discount.
0.80x0.80x
A 20%20\% discount means the buyer pays 100%−20%=80%100\% - 20\% = 80\% of the original price xx.
2
Set up an expression for the price after the second discount.
0.72x0.72x
An additional 10%10\% discount means the buyer pays 90%90\% of the already discounted price. Multiplying 0.90×0.80x0.90 \times 0.80x gives 0.72x0.72x.
3
Set the final expression equal to the sale price and solve for the original price.
0.72x=360⇒x=5000.72x = 360 \Rightarrow x = 500
This isolates the original price, xx, finding the initial value before any markdowns.

Key Concept

Calculating successive discounts and setting up an equation to find the original pre-sale price.
Question 18Question →

A landscaping company is purchasing a bulk order of premium grass seed. The wholesale price of the order is $550\$550. The supplier offers a 20%20\% commercial discount on the order. After the discount is applied, a 5%5\% sales tax is added. What is the final total cost of the grass seed order?

Show answer & explanation

Answer: $462.00\$462.00

Answer

The final total cost of the grass seed order is $462.00\$462.00.
The correct answer is found by completing the calculation in two distinct steps. First, apply the 20%20\% discount to the original $550\$550 price ($550×0.80=$440\$550 \times 0.80 = \$440). Second, calculate the 5%5\% sales tax on the new $440\$440 balance and add it to the cost ($440×1.05=$462.00\$440 \times 1.05 = \$462.00).

Step-by-Step Solution

1
Calculate the discount amount by finding 20%20\% of $550\$550.
$550×0.20=$110\$550 \times 0.20 = \$110
The commercial discount reduces the original wholesale price by a percentage.
2
Subtract the discount amount from the original price to find the sale price.
$550−$110=$440\$550 - \$110 = \$440
This establishes the actual price of the grass seed before sales tax is applied.
3
Calculate the 5%5\% sales tax on the discounted sale price.
$440×0.05=$22\$440 \times 0.05 = \$22
Sales tax must be applied to the final sale price, not the original sticker price.
4
Add the sales tax to the sale price to find the final total cost.
$440+$22=$462.00\$440 + \$22 = \$462.00
The final cost includes both the discounted price and the applicable tax.

Key Concept

Calculating multi-step financial arithmetic problems involving sequential discounts and sales taxes.
Question 19Question →

A carpenter is purchasing a commercial-grade table saw. The original price of the table saw is $850\$850. The store offers a 20%20\% discount on all power tools. After the discount is applied, a 5%5\% sales tax is added to the purchase price. What is the final total amount the carpenter pays for the table saw?

Show answer & explanation

Answer: $714.00\$714.00

Answer

$714.00\$714.00
To find the final price, first determine the sale price by taking 20%20\% off the original $850\$850. Since 20%20\% of $850\$850 is $170\$170, the discounted price is $680\$680. Next, apply the 5%5\% sales tax to the new sale price of $680\$680. The tax is 0.05×$680=$340.05 \times \$680 = \$34. Adding the tax to the sale price gives the final total of $714.00\$714.00.

Step-by-Step Solution

1
Calculate the discount amount.
$170\$170
The discount is 20%20\% of the original price: 0.20×$850=$1700.20 \times \$850 = \$170.
2
Determine the discounted sale price.
$680\$680
Subtract the discount amount from the original price: $850−$170=$680\$850 - \$170 = \$680.
3
Calculate the sales tax amount on the sale price.
$34\$34
The tax is 5%5\% of the discounted price: 0.05×$680=$340.05 \times \$680 = \$34.
4
Calculate the final total amount.
$714.00\$714.00
Add the sales tax to the sale price: $680+$34=$714\$680 + \$34 = \$714.

Key Concept

Discounts and Sale Prices
Question 20Question →

A bakery owner is purchasing a new commercial dough mixer. The original price of the mixer is $1,500\$1,500. The restaurant supply store is running a promotional sale offering a 20%20\% discount on all equipment. Additionally, the owner receives an extra 10%10\% discount on the sale price for paying directly through a business bank transfer. What is the final sale price of the dough mixer in dollars?

Show answer & explanation

Answer: 1080

Answer

The final sale price of the dough mixer is $1,080\$1,080.
To find the final price after successive discounts, each discount must be applied sequentially to the updated balance. First, applying the 20%20\% discount to the original $1,500\$1,500 price reduces it by $300\$300, resulting in an intermediate sale price of $1,200\$1,200. The subsequent 10%10\% discount is then applied to this new $1,200\$1,200 balance, taking off an additional $120\$120. Subtracting $120\$120 from $1,200\$1,200 yields a final price of $1,080\$1,080.

Step-by-Step Solution

1
Calculate the amount of the first discount.
$1,500×0.20=$300\$1,500 \times 0.20 = \$300
The promotional discount applies to the original base price.
2
Determine the intermediate sale price after the first discount.
$1,500−$300=$1,200\$1,500 - \$300 = \$1,200
Subtracting the discount from the original price gives the new price before further markdowns.
3
Calculate the amount of the second discount.
$1,200×0.10=$120\$1,200 \times 0.10 = \$120
Successive discounts are calculated based on the new reduced sale price, not the original price.
4
Determine the final price after the second discount.
$1,200−$120=$1,080\$1,200 - \$120 = \$1,080
Subtracting the second discount from the intermediate price yields the final amount owed.

Key Concept

Successive/Chain Discounts
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Discounts and Sale Prices Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB) | Examkin