A store owner purchases an item from a wholesaler. She increases the wholesaler's cost by … — SAT

A store owner purchases an item from a wholesaler. She increases the wholesaler's cost by $40\%$ to set the retail price of the item. During a clearance sale, the retail price is discounted by $20\%$ . If the clearance sale price of the item is $84.00$ dollars, what was the wholesaler's cost of the item, in dollars?

A
70
75Answer
C
63
D
72

Answer

The correct answer is

75

. The relationship between the wholesaler's cost

C

, the retail price, and the clearance price is

C \times 1.40 \times 0.80 = 84

. Simplifying the expression yields

1.12C = 84

, which solves to

C = 75

Step-by-Step Solution

Represent the retail price in terms of the wholesaler's cost

C

Retail price =

1.40C

The retail price represents a

40\%

markup on the original wholesaler's cost.

Represent the clearance sale price in terms of the retail price.

Clearance price =

0.80 \times (1.40C) = 1.12C

20\%

discount reduces the price to

80\%

of the retail price.

Set up the equation using the given clearance sale price of

84.00

dollars and solve for

C

1.12C = 84 \implies C = \frac{84}{1.12} = 75

Dividing the sale price by the net percentage factor isolates the initial cost.

Key Concept

Applying consecutive percentage changes to find an unknown initial value.

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic