At a clothing retailer, the wholesale cost of a leather coat was 50\% greater than the who… — GRE General Test

At a clothing retailer, the wholesale cost of a leather coat was $50\%$ greater than the wholesale cost of a denim jacket. The following year, the wholesale cost of the leather coat increased by $20\%$ , while the wholesale cost of the denim jacket decreased by $10\%$ . What was the overall percentage increase in the combined wholesale cost of one leather coat and one denim jacket?

A
$2\%$
B
$5\%$
$8\%$ Answer
D
$10\%$
E
$15\%$

Answer

An overall increase of

8\%

in the combined wholesale cost.

Assuming an initial denim jacket cost of

100

, the leather coat costs

150

, giving an initial combined cost of

250

. After a

20\%

increase, the coat costs

180

, and after a

10\%

decrease, the jacket costs

90

. The new combined total is

270

. The total increase is

20

, which represents

\frac{20}{250} = 8\%

of the original combined cost.

Step-by-Step Solution

Define variables for the initial costs of the items.

Let the initial cost of the denim jacket be

d = 100

. Then the initial cost of the leather coat is

1.50d = 150

Choosing a convenient base value makes calculating relative percentage changes straightforward.

Calculate the initial total cost and the new individual costs after price changes.

Initial total cost =

100 + 150 = 250

. New cost of leather coat =

150 \times (1 + 0.20) = 180

. New cost of denim jacket =

100 \times (1 - 0.10) = 90

Percentage increases and decreases must be applied to their respective starting costs.

Compute the new combined total cost and calculate the net percentage change.

New combined total cost =

180 + 90 = 270

. Dollar change =

270 - 250 = 20

. Net percentage increase =

\frac{20}{250} \times 100\% = 8\%

Percent change is calculated by dividing the absolute change by the original combined base value.

Key Concept

Combined Percent Change and Weighted Base Values

Question

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Key Concept

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