Solve the following problem by determining the missing value. Enter your final numerical a… — Armed Services Vocational Aptitude Battery (ASVAB)

Solve the following problem by determining the missing value. Enter your final numerical answer in the blank provided.

Cevap:A base exchange purchases a batch of tactical backpacks from a distributor. The exchange applies a markup of

60\%

over the distributor cost to determine the standard price. After a month, the backpacks are placed on clearance, reducing the standard price by

30\%

. A service member buys a backpack using a special coupon that takes an additional

15\%

off the clearance price. If the service member pays

\$66.64

for the backpack (which is tax-exempt), the original distributor cost of the backpack was

\$【70】

The original cost is found by translating the successive markup and discounts into multipliers:

1.60

for the

60\%

markup,

0.70

for the

30\%

discount, and

0.85

for the

15\%

discount. The product of these multipliers is

1.60 \times 0.70 \times 0.85 = 0.952

. This means the final price is

95.2\%

of the original cost. Setting

0.952C = \$66.64

and dividing gives the original distributor cost of

\$70

Define a variable for the unknown original cost.

Let

C

represent the original distributor cost of the backpack.

Setting up a variable allows us to build an algebraic equation to track the successive price changes.

Calculate the multiplier for the

60\%

markup.

Standard Price =

C \times (1 + 0.60) = 1.60C

A markup increases the cost by that percentage, making the new price

160\%

of the original cost.

Apply the

30\%

clearance discount to the standard price.

Clearance Price =

1.60C \times (1 - 0.30) = 1.60C \times 0.70 = 1.12C

The clearance reduction applies to the newly established standard price, leaving

70\%

of that price.

Apply the additional

15\%

coupon discount to the clearance price.

Final Price =

1.12C \times (1 - 0.15) = 1.12C \times 0.85 = 0.952C

The coupon applies sequentially to the clearance price, meaning the customer pays

85\%

of that discounted amount.

Set the final price expression equal to the known amount paid and solve for

C

0.952C = 66.64 \Rightarrow C = \frac{66.64}{0.952} = 70

Equating the algebraic expression to the actual dollar amount allows us to isolate and calculate the original distributor cost.

Solving multi-step percentage changes by applying successive multipliers to find an unknown base value.

Soru