Financial Arithmetic Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB) — Page 6

Question 101Question →

A field medical unit needs to resupply liquid surface disinfectant. The disinfectant is available in four different packaging options. Arrange the purchasing options in order from the lowest unit price (price per gallon) to the highest unit price.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct order from lowest to highest unit price is: the pack of eight 1-pint bottles (

\$23.04

/gal), the twin-pack of two 1-gallon jugs (

\$24.00

/gal), the 5-gallon drum (

\$25.60

/gal), and the case of four 1-quart bottles (

\$28.16

/gal).

By converting the capacity of each option to a common unit (gallons) and calculating the price per gallon, we can directly compare the unit costs. The

1

-pint bottles equate to

1

gallon for

\$23.04

. The

1

-gallon jugs cost

\$24.00

per gallon (

\$48.00 \div 2

). The

5

-gallon drum costs

\$25.60

per gallon (

\$128.00 \div 5

). The

1

-quart bottles equate to

1

gallon for

\$28.16

. Placing these calculated unit prices in ascending order provides the correct sequence.

Step-by-Step Solution

1

Determine a common unit of measurement to compare all options.

The gallon is the most convenient common unit.

Converting all volumes to gallons allows for a direct dollar-to-dollar comparison of the unit prices.

2

Calculate the price per gallon for the

5

-gallon drum.

\$128.00 \div 5 \text{ gallons} = \$25.60

per gallon.

Dividing the total cost by the total volume yields the unit price.

3

Calculate the price per gallon for the case of

1

-quart bottles.

There are

4

quarts in a gallon, so four

1

-quart bottles equal exactly

1

gallon. The price is

\$28.16

per gallon.

Unit conversion is required before finding the price per gallon.

4

Calculate the price per gallon for the pack of

1

-pint bottles.

There are

2

pints in a quart and

4

quarts in a gallon, so there are

8

pints in a gallon. Eight

1

-pint bottles equal exactly

1

gallon. The price is

\$23.04

per gallon.

Unit conversion is required to establish the total volume in gallons.

5

Calculate the price per gallon for the twin-pack of

1

-gallon jugs.

\$48.00 \div 2 \text{ gallons} = \$24.00

per gallon.

Dividing the total cost by the total volume yields the unit price.

6

Compare the calculated prices per gallon and order them from lowest to highest.

\$23.04 < \$24.00 < \$25.60 < \$28.16

.

The question asks for the options to be arranged sequentially by increasing unit cost.

Key Concept

To compare the prices of items sold in different quantities and unit sizes, convert all volumes to a single common unit (such as gallons) and calculate the price per common unit for each option.

Question 102Question →

A local hardware store is purchasing a bulk wholesale order of industrial shelving. The distributor offers a $20\%$ volume discount on the order. Because the hardware store pays the invoice in full within 10 days, they receive an additional $5\%$ discount on the reduced price. If the hardware store pays $\$3,420$ for the shelving (before shipping and taxes), what was the original price of the bulk order?

\$3,445

\$4,275

\$4,500

\$4,560

Show answer & explanation

Answer: $\$4,500$

Answer

\$4,500

The correct answer is found by representing the unknown original price as a variable, applying the 20% discount (multiplying by 0.80), and then applying the 5% discount to that new amount (multiplying by 0.95). Setting the resulting expression (0.76 times the original price) equal to the final price of

3,420 and dividing yields an original price of

4,500.

Step-by-Step Solution

1

Set up an equation representing the first discount.

Let the original price be

P

. A

20\%

discount means the price becomes

100\% - 20\% = 80\%

of the original price, or

0.80P

.

The volume discount is applied to the starting original price.

2

Apply the second successive discount to the result of the first.

An additional

5\%

discount on the reduced price means the hardware store pays

100\% - 5\% = 95\%

of that reduced price. This gives

0.95 \times 0.80P = 0.76P

.

Successive discounts are calculated based on the new, already-discounted price, not the original price.

3

Solve for the original price

P

.

Set the expression equal to the final paid amount:

0.76P = 3420

. Divide both sides by

0.76

to find

P = \$4,500

.

This isolates

P

to determine the starting value before any discounts were applied.

Key Concept

Calculating the original price after successive discounts by working backward using algebraic representation.

Question 103Question →

A maintenance supervisor is ordering floor sealant for a large building renovation. The sealant is available in two sizes: a $2$ -gallon jug priced at $\$18.00$ , and a $1$ -quart bottle priced at $\$3.25$ . If the renovation requires exactly $8$ gallons of sealant, how much money is saved in total by purchasing the $2$ -gallon jugs instead of the $1$ -quart bottles?

\$4.00

\$46.00

\$32.00

\$61.60

Show answer & explanation

Answer: $\$32.00$

Answer

\$32.00

To find the total savings, calculate the total cost for each option. For the

2

-gallon jugs, you need

4

jugs to reach

8

gallons (

4 \times \$18.00 = \$72.00

). For the

1

-quart bottles, first convert

8

gallons to quarts (

8 \times 4 = 32

quarts). You need

32

bottles (

32 \times \$3.25 = \$104.00

). The difference is

\$104.00 - \$72.00 = \$32.00

.

Step-by-Step Solution

1

Calculate the total cost of purchasing 8 gallons using the 2-gallon jugs.

\$72.00

The project needs 8 gallons, which requires 4 jugs (

8 \div 2

). At

\$18.00

per jug, the cost is

4 \times \$18.00 = \$72.00

.

2

Determine how many 1-quart bottles are needed to make 8 gallons.

32 bottles

There are 4 quarts in 1 gallon, so 8 gallons is equal to 32 quarts (

8 \times 4

).

3

Calculate the total cost of purchasing 32 quart bottles.

\$104.00

At

\$3.25

per bottle, the cost is

32 \times \$3.25 = \$104.00

.

4

Calculate the total savings between the two options.

\$32.00

Subtract the lower bulk cost from the higher individual cost:

\$104.00 - \$72.00 = \$32.00

.

Key Concept

Unit Price Comparisons

Question 104Question →

A base landscaping crew needs to purchase concentrated herbicide. Vendor A sells a $5$ -gallon drum of the herbicide for $\$140.00$ . Vendor B sells the same herbicide in $2$ -quart bottles for $\$15.00$ each. What is the difference in price per gallon, in dollars, between the two vendors?

Show answer & explanation

Answer: 2

Answer

The difference in price per gallon between the two vendors is 2 dollars.

By converting both options to a common unit price of dollars per gallon, we find Vendor A charges

28.00 per gallon and Vendor B charges

30.00 per gallon. The difference between these unit prices is

30.00 -

28.00 = $2.00.

Step-by-Step Solution

1

Calculate the price per gallon for Vendor A.

\$140.00 \div 5 \text{ gallons} = \$28.00 \text{ per gallon}

To compare prices accurately, both must be expressed as a unit rate (price per gallon).

2

Convert the volume of Vendor B's bottles into gallons to find how many bottles equal one gallon.

Since there are

4 \text{ quarts}

in

1 \text{ gallon}

, a

2

-quart bottle is

0.5 \text{ gallons}

. Therefore, it takes

2

bottles to make

1 \text{ gallon}

.

Unit prices must be in the same measurement (gallons) for a valid comparison.

3

Calculate the price per gallon for Vendor B.

\$15.00 \times 2 \text{ bottles} = \$30.00 \text{ per gallon}

This establishes the unit rate for Vendor B.

4

Find the difference between the two unit prices.

\$30.00 - \$28.00 = \$2.00

The question asks for the numeric difference in price per gallon.

Key Concept

Comparing unit prices by converting to a common unit of measure.

Question 105Question →

Read the scenario below and fill in the missing financial values.

Fill in the blanks below

A musician is purchasing a new drum kit for

\$1,200

and a set of cymbals for

\$400

. The music store is running a promotion that offers a

15\%

discount on the total purchase if it exceeds

\$1,000

. After the discount is applied, a

6\%

state sales tax is added to the sale price.

Based on this information, the total amount saved from the discount is $\$

, and the final amount paid after tax is

\$$.

Show answer & explanation

Answer

The discount amount is

\$240

, and the final total paid is

\$1,441.60

.

The solution requires finding the total original price of

\$1,600

. The

15\%

discount on this amount is

\$240

, leaving a sale price of

\$1,360

. Finally, calculating a

6\%

sales tax on

\$1,360

adds

\$81.60

, bringing the final total to

\$1,441.60

.

Step-by-Step Solution

1

Calculate the total original price of the items.

\$1,200 + \$400 = \$1,600

To find the base amount before any discounts are applied.

2

Calculate the discount amount.

15\%

of

\$1,600 = 0.15 \times 1600 = \$240

Since the purchase exceeds

\$1,000

, the

15\%

discount applies to the total original price. This provides the first missing value.

3

Calculate the sale price before tax.

\$1,600 - \$240 = \$1,360

Subtracting the discount from the original price gives the taxable amount.

4

Calculate the sales tax.

6\%

of

\$1,360 = 0.06 \times 1360 = \$81.60

Sales tax is calculated based on the discounted sale price.

5

Calculate the final total paid.

\$1,360 + \$81.60 = \$1,441.60

Adding the sales tax to the sale price yields the final cost. This provides the second missing value.

Key Concept

Calculating a percentage discount on a total sum and then applying sales tax to the discounted price.

Alternative Method

You can calculate the final price in one continuous equation by multiplying the original price by the complement of the discount (

1 - 0.15 = 0.85

) to get the sale price, and then multiplying by the tax multiplier (

1 + 0.06 = 1.06

):

\$1,600 \times 0.85 \times 1.06 = \$1,441.60

.

Estimated Time:1m 30s

Question 106Question →

A fleet manager is purchasing a replacement heavy-duty transmission. The original price of the transmission is $\$3,200$ . The supplier offers a $15\%$ commercial discount, and an additional $5\%$ discount off the reduced price if the invoice is paid within $10$ days. If the manager pays the invoice on the same day, what is the final price of the transmission before any taxes?

\$2,560

\$2,584

\$616

\$3,180

Show answer & explanation

Answer: $\$2,584$

Answer

The final price of the transmission is

\$2,584

.

The correct answer accurately calculates the successive discounts step by step. First, a

15\%

discount on

\$3,200

saves

\$480

, bringing the price to

\$2,720

. Then, a

5\%

discount on the new price of

\$2,720

saves

\$136

, resulting in a final price of

\$2,584

.

Step-by-Step Solution

1

Calculate the price after the first discount of

15\%

.

\$3,200 \times 0.15 = \$480

in savings. The new price is

\$3,200 - \$480 = \$2,720

.

The commercial discount is applied to the original price of the item.

2

Calculate the final price after the second discount of

5\%

.

\$2,720 \times 0.05 = \$136

in savings. The final price is

\$2,720 - \$136 = \$2,584

.

Successive (chain) discounts are always applied to the previously reduced price, not the original price.

Key Concept

Discounts and Sale Prices

Question 107Question →

A motor pool sergeant is purchasing industrial degreaser for the vehicle maintenance bay. The facility requires exactly $8$ gallons of degreaser. A supply catalog offers the degreaser in two sizes: a $1$ -gallon jug for $\$14.50$ and a $32$ -ounce bottle for $\$4.00$ . If the sergeant purchases the required amount using the most cost-effective option, how much money will be saved in total compared to buying the more expensive option?

\$1.20

\$12.00

\$84.00

\$108.00

Show answer & explanation

Answer: $\$12.00$

Answer

\$12.00

The correct answer is found by first equalizing the volumes. There are 128 ounces in a gallon, so it takes four 32-ounce bottles to make a single gallon. Buying the degreaser in bottles costs 4 ×

4.00 =

16.00 per gallon. The 1-gallon jug costs

14.50, meaning the jug saves

1.50 per gallon compared to the bottles. Because the facility needs 8 gallons, the total savings is 8 ×

1.50 =

12.00.

Step-by-Step Solution

1

Determine the number of 32-ounce bottles needed to equal one gallon.

Since

1

gallon equals

128

ounces,

128 \div 32 = 4

bottles per gallon.

To accurately compare prices, both options must be evaluated at the same unit of volume.

2

Calculate the price per gallon for the 32-ounce bottle option.

4

bottles

\times \$4.00 = \$16.00

per gallon.

This establishes a direct unit price comparison against the 1-gallon jug.

3

Determine which option is more cost-effective and calculate the savings per gallon.

The jug costs

\$14.50

per gallon, which is

\$1.50

cheaper than the

\$16.00

per gallon cost of the bottles.

Finding the difference in unit price is necessary to calculate the total savings over the entire purchase.

4

Calculate the total savings for the required 8 gallons.

8

gallons

\times \$1.50 = \$12.00

total savings.

The facility requires 8 gallons, so the per-gallon savings must be multiplied by the total volume needed.

Key Concept

Comparing unit prices across different measurement units to find total purchase savings.

Question 108Question →

A commercial photographer is purchasing a new studio lighting kit. The original retail price of the kit is $\$1,200$ . The camera supply store is currently offering a $25\%$ seasonal discount on all studio equipment. In addition, the photographer receives a $10\%$ professional discount, which is applied to the already reduced price. What is the final price of the lighting kit before sales tax?

Show answer & explanation

Answer: 810

Answer

The final price of the lighting kit is

\$810

.

The correct calculation requires applying the first discount to find a new subtotal, and then applying the second discount to that new subtotal. Applying

25\%

off

\$1,200

yields

\$900

. Applying the

10\%

professional discount to the new base of

\$900

reduces the price by another

\$90

, resulting in a final price of

\$810

.

Step-by-Step Solution

1

Calculate the first discount amount.

25\%

of

\$1,200

is

\$300

.

The seasonal discount applies to the original retail price.

2

Find the intermediate reduced price.

\$1,200 - \$300 = \$900

.

Subtracting the first discount gives the new base price before the second discount.

3

Calculate the second discount amount.

10\%

of

\$900

is

\$90

.

The professional discount applies to the already reduced price, not the original price.

4

Determine the final price.

\$900 - \$90 = \$810

.

Subtracting the second discount from the intermediate price gives the final amount paid.

Key Concept

Calculating successive discounts requires applying the second percentage to the new, already discounted price, rather than the original amount.

Question 109Question →

A cafe owner is purchasing a commercial espresso machine. Supplier A lists the machine for $\$2,000$ with a single $30\%$ discount. Supplier B lists the identical machine for $\$2,400$ with successive discounts of $25\%$ and $20\%$ . How much money will the owner save by purchasing the machine from the less expensive supplier?

\$385

\$40

\$80

\$360

Show answer & explanation

Answer: $\$40$

Answer

The owner will save $40 by choosing Supplier A.

Supplier A's final price is

1,400 (which is

2,000 minus a

600 discount). Supplier B's final price is

1,440 (calculated by first reducing

2,400 by 25% to get

1,800, and then reducing

1,800 by 20% to get

1,440). The difference between the two prices is $40, making Supplier A the less expensive option by that amount.

Step-by-Step Solution

1

Calculate the final price for Supplier A.

\$2,000 \times 0.30 = \$600

discount.

\$2,000 - \$600 = \$1,400

.

A single discount is taken directly from the initial price.

2

Calculate the price after the first discount for Supplier B.

\$2,400 \times 0.25 = \$600

discount.

\$2,400 - \$600 = \$1,800

.

The first of the successive discounts is applied to the original listing price.

3

Calculate the price after the second discount for Supplier B.

\$1,800 \times 0.20 = \$360

discount.

\$1,800 - \$360 = \$1,440

.

The second discount must be applied to the new subtotal, not the original price.

4

Find the difference between the two final prices.

\$1,440 - \$1,400 = \$40

.

Subtracting the lower price from the higher price gives the total savings.

Key Concept

Calculating successive discounts and comparing final sale prices.

Question 110Question →

An auto repair shop owner orders a bulk supply of replacement brake pads with an original total cost of $\$800$ . The automotive parts distributor applies a $15\%$ bulk discount to the order. In addition, the shop receives an extra $5\%$ discount on the reduced price for paying the invoice in full upon delivery.

Determine the shop's final purchase price for the brake pads and the total amount of money saved compared to the original cost.

Fill in the blanks below

The final purchase price is $\$

and the total amount saved is

\$$.

Show answer & explanation

Answer

The final purchase price is

646 and the total amount saved is

154.

The correct final price is found by taking 15% off

800 to get

680, then taking 5% off

680 to arrive at

646. The total savings is the sum of both discounts (

120 +

34 = $154).

Step-by-Step Solution

1

Calculate the amount of the 15% bulk discount.

\$800 \times 0.15 = \$120

To find the savings provided by the initial distributor discount.

2

Calculate the intermediate price after the first discount.

\$800 - \$120 = \$680

The subsequent 5% discount must be applied to this reduced price, not the original price.

3

Calculate the amount of the 5% payment discount.

\$680 \times 0.05 = \$34

To determine the additional savings from paying the invoice in full upon delivery.

4

Calculate the final purchase price.

\$680 - \$34 = \$646

This is the final amount the shop must pay after all successive discounts have been applied.

5

Calculate the total amount saved.

\$120 + \$34 = \$154

To find the complete difference between the original cost and the final price.

Key Concept

Successive discounts must be calculated sequentially on the new reduced price at each step, rather than adding the percentages together.

Question 111Question →

A restaurant manager orders a bulk supply of premium cooking oil. The invoice shows a final cost of $\$510$ after a $15\%$ wholesale discount was applied to the standard price. What was the original standard price of the bulk supply before the discount?

\$586.50

\$600.00

\$433.50

\$525.00

Show answer & explanation

Answer: $\$600.00$

Answer

The original standard price of the bulk supply was $600.00.

The final cost of

510 represents 85% of the original price, because a 15% discount was subtracted (100% - 15% = 85%). To find the original whole amount, divide the part by the percentage as a decimal:

510 \div 0.85 = \

600

.

Step-by-Step Solution

1

Determine the percentage of the original price that the final cost represents.

Since a

15\%

discount was applied, the manager paid

100\% - 15\% = 85\%

of the original price.

The final discounted price represents the remainder of the original cost after the discount is subtracted.

2

Set up an equation and solve for the original price.

Let

x

be the original price. The equation is

0.85x = 510

. Solving for

x

gives

x = 510 \div 0.85 = 600

.

Dividing the part (the discounted price) by its equivalent percentage (expressed as a decimal) gives the whole original amount.

Key Concept

To find the original price before a discount, divide the final discounted price by the complement of the discount percentage (100% minus the discount rate).

Question 112Question →

An IT director is upgrading a company's data center and orders 4 new enterprise servers. The original retail price for each server is $\$4,500$ . The hardware supplier offers a $20\%$ corporate discount on the total order. Additionally, because the company pays the invoice in full within 10 days, a $5\%$ early-payment discount is applied to the already reduced price. What is the final total price, in dollars, paid for the servers?

Show answer & explanation

Answer: 13680

Answer

13680

The correct total is found by first determining the initial total order value (

\$18,000

), reducing it by the initial

20\%

discount to find the new subtotal (

\$14,400

), and then reducing that subtotal by the additional

5\%

discount to arrive at the final cost (

\$13,680

).

Step-by-Step Solution

1

Calculate the total original price of the 4 servers.

4 \times \$4,500 = \$18,000

The discounts apply to the total order, so the total initial cost must be determined first.

2

Apply the 20% corporate discount to the total original price.

\$18,000 \times 0.20 = \$3,600 \text{ discount; } \$18,000 - \$3,600 = \$14,400

The first discount reduces the total cost before any other discounts are considered.

3

Apply the 5% early-payment discount to the new, reduced price.

\$14,400 \times 0.05 = \$720 \text{ discount; } \$14,400 - \$720 = \$13,680

Successive discounts are applied sequentially to the most recently calculated price, not the original price.

Key Concept

Calculating successive discounts on a total order amount.

Estimated Time:1m 30s

Question 113Question →

A diner's meal costs $50.00. If the diner leaves a 20% tip, what is the total amount paid?

$10.00

$51.00

$60.00

$70.00

Show answer & explanation

Answer: $60.00

Answer

$60.00

The correct total is found by converting 20% to a decimal (0.20), multiplying it by

50.00 to find the tip amount (

10.00), and then adding that tip to the original

50.00 bill to get a total of

60.00.

Step-by-Step Solution

1

Calculate the amount of the tip by finding 20% of the meal cost ($50.00).

$10.00

The tip is a percentage based on the initial cost of the meal.

2

Add the tip amount to the original meal cost.

$60.00

The total amount paid includes both the original meal cost and the tip.

Key Concept

Calculating a percentage of a quantity and adding it to the base amount.

Question 114Question →

Read the scenario and fill in the missing numerical values.

Fill in the blanks below

A customer gets a haircut that costs

\$20.00

. If the customer leaves a

15\%

tip, the tip amount is $\$

and the total cost of the haircut is

\$$.

Show answer & explanation

Answer

The tip amount is

3.00 and the total cost is

23.00.

The tip amount is found by multiplying the base cost by the tip percentage expressed as a decimal (

\$20.00 \times 0.15 = \$3.00

). The total cost is determined by adding this calculated tip amount to the original price (

\$20.00 + \$3.00 = \$23.00

).

Step-by-Step Solution

1

Convert the tip percentage to a decimal and multiply by the cost of the haircut.

\$20.00 \times 0.15 = \$3.00

To find the dollar amount of the tip, calculate

15\%

of the original price.

2

Add the calculated tip amount to the original cost.

\$20.00 + \$3.00 = \$23.00

The total cost is the sum of the original service price and the tip.

Key Concept

Calculating tip amounts using percentages and finding the final total cost.

Question 115Question →

Marcus purchases a tool set with a price tag of $40.00. If the hardware store applies a 5% sales tax, what is the final amount Marcus must pay?

$42.00

$45.00

$60.00

$2.00

Show answer & explanation

Answer: $42.00

Answer

The total cost of the tool set including tax is $42.00.

To find the final amount, you must calculate the sales tax and add it to the original price. 5% of

40.00 is

2.00. Adding this

2.00 tax to the

40.00 price tag yields a total of $42.00.

Step-by-Step Solution

1

Calculate the amount of sales tax by finding 5% of $40.00.

40.00 \times 0.05 =

2.00

Sales tax is a percentage of the original price.

2

Add the calculated sales tax to the original price to find the final total.

40.00 +

2.00 = $42.00

The total amount paid includes both the item's price and the tax applied to it.

Key Concept

Calculating sales tax as a percentage and adding it to the base price to determine the total cost.

Estimated Time:45s

Question 116Question →

A customer purchases a tablet with an original price of $300.00. The tablet is on sale for 20% off. After the discount is applied, a 5% sales tax is added to the sale price. What is the final total cost of the tablet?

$241.20

$252.00

$255.00

$294.00

Show answer & explanation

Answer: $252.00

Answer

$252.00

To find the total cost, first find the sale price by calculating 20% of

300.00, which is

60.00. Subtract this discount from the original price to get

240.00. Next, calculate the 5% sales tax on this new sale price: 0.05 ×

240.00 =

12.00. Finally, add the tax to the sale price:

240.00 +

12.00 =

252.00.

Step-by-Step Solution

1

Calculate the discount amount.

20% of

300.00 = 0.20 ×

300.00 = $60.00

The discount must be determined to find the sale price.

2

Subtract the discount from the original price.

300.00 -

60.00 = $240.00

This provides the discounted sale price upon which tax is calculated.

3

Calculate the sales tax on the sale price.

5% of

240.00 = 0.05 ×

240.00 = $12.00

Sales tax is always applied to the final discounted price of the item.

4

Add the sales tax to the sale price.

240.00 +

12.00 = $252.00

This determines the final total cost the customer must pay.

Key Concept

Calculating sequential percentages in multi-step financial problems (applying discounts before taxes).

Alternative Method

You can solve this using multipliers in a single step: Total Cost = Original Price × (1 - Discount Rate) × (1 + Tax Rate). Here,

300.00 × 0.80 × 1.05 =

252.00.

Estimated Time:1m 30s

Question 117Question →

Sarah's family goes out for dinner, and the total food bill is $60.00. They decide to leave a 15% tip for the server. How much money, in dollars, do they leave for the tip?

Show answer & explanation

Answer: 9

Answer

9

The tip amount is found by calculating 15% of

60.00. By multiplying

60.00

by

0.15

, the result is

9.00$, which represents the tip amount in dollars.

Step-by-Step Solution

1

Convert the tip percentage into a decimal.

15\% = 0.15

Percentages must be converted to decimals to perform multiplication.

2

Multiply the total bill by the decimal tip rate.

60.00 \times 0.15 = 9.00

The tip amount is a percentage of the total bill.

Key Concept

Calculating a percentage of a given monetary amount.

Question 118Question →

A group of friends goes out for dinner. The total bill comes to $74.40, which includes a 6% sales tax and an 18% tip. If both the tax and the tip were calculated based on the original cost of the food, what was the cost of the food before the tax and tip were added?

Fill in the blanks below

The original cost of the food was $.

Show answer & explanation

Answer

The original cost of the food was $60.00.

By adding the 6% sales tax and the 18% tip, we find that a total of 24% was added to the original cost. This means the final bill of

74.40 is equal to 124% (or 1.24 times) the original food cost. Dividing

74.40 by 1.24 gives the correct original cost of $60.00.

Step-by-Step Solution

1

Determine the combined percentage rate applied to the original cost.

Combined percentage = 6% tax + 18% tip = 24%.

Since both the tax and the tip are based on the original food cost, their percentages can be added together.

2

Express the total bill as a percentage of the original cost.

The total bill represents 100% of the original cost plus the 24% in additions, which equals 124% of the original cost.

The final amount includes the original base amount (100%) and the additional charges.

3

Set up an equation and solve for the original cost.

Let x be the original cost. 1.24x = $74.40. Dividing both sides by 1.24 gives x = 60.

Converting 124% to a decimal (1.24) and dividing the final amount by this multiplier isolates the original pre-tax cost.

Key Concept

Calculating an original base price by dividing the final total by a growth factor multiplier (1 + combined percentage rate).

Question 119Question →

A contractor is purchasing supplies for a project. He buys a power drill originally priced at $\$150.00$ and a set of drill bits originally priced at $\$50.00$ . The drill is on sale for $30\%$ off, but the drill bits are sold at full price. If an $8\%$ sales tax is applied to the entire purchase after the discount is taken, what is the final total amount paid?

\$171.00

\$156.24

\$167.40

\$151.20

Show answer & explanation

Answer: $\$167.40$

Answer

\$167.40

The correct amount is found by first calculating the

30\%

discount on the

\$150.00

drill, which is a

\$45.00

reduction, making the drill

\$105.00

. Adding the full-price

\$50.00

drill bits brings the subtotal to

\$155.00

. Finally, calculating the

8\%

sales tax on the

\$155.00

subtotal gives

\$12.40

. Adding the tax to the subtotal yields the final amount of

\$167.40

.

Step-by-Step Solution

1

Calculate the discount amount for the power drill.

\$150.00 \times 0.30 = \$45.00

To determine how much will be reduced from the drill's original price.

2

Determine the sale price of the power drill.

\$150.00 - \$45.00 = \$105.00

To find the actual cost of the drill before tax.

3

Calculate the pre-tax subtotal for all purchased items.

\$105.00 \text{ (drill)} + \$50.00 \text{ (bits)} = \$155.00

The sales tax is applied to the combined cost of the discounted and full-priced items.

4

Calculate the sales tax on the subtotal.

\$155.00 \times 0.08 = \$12.40

An 8% tax applies to the entire pre-tax subtotal.

5

Calculate the final total amount paid.

\$155.00 + \$12.40 = \$167.40

The final total must include both the purchase subtotal and the applied sales tax.

Key Concept

Calculating multi-step financial transactions involving partial-order discounts and subsequent aggregate sales tax.

Question 120Question →

An electrician buys some wiring supplies that total $150.00 before tax. If the local sales tax rate is 8%, what is the total cost of the supplies including tax?

$12.00

$158.00

$162.00

$270.00

Show answer & explanation

Answer: $162.00

Answer

$162.00

The correct answer is found by first calculating the sales tax, which is 8% of the

150.00 subtotal. Multiplying

150.00 by 0.08 gives a tax amount of

12.00. Then, this tax amount is added to the original cost (

150.00 +

12.00) to find the final total of

162.00.

Step-by-Step Solution

1

Calculate the amount of sales tax.

\$150.00 \times 0.08 = \$12.00

To find the tax, multiply the pre-tax cost by the decimal form of the percentage (8% = 0.08).

2

Add the tax amount to the original cost.

\$150.00 + \$12.00 = \$162.00

The total cost includes both the base price and the applied sales tax.

Key Concept

Calculating Sales Tax and Total Cost

Financial Arithmetic

Answer

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