A retailer purchased a shipment of coats for a wholesale price of x dollars each. The reta… — SAT

A retailer purchased a shipment of coats for a wholesale price of $x$ dollars each. The retailer marked up the wholesale price by $40\%$ to determine the retail price. During a winter sale, the retailer offered a discount of $20\%$ off the retail price of the coats. If the sale price of a coat was $84$ dollars, what was the wholesale price, $x$ , of the coat?

A
$63$
B
$70$
$75$ Answer
D
$80$

Answer

75

The correct answer is

75

. The retail price is determined by increasing the wholesale price,

x

, by

40\%

, which can be represented as

1.40x

. The sale price is determined by decreasing the retail price by

20\%

, which is

0.80(1.40x) = 1.12x

. Since the sale price of the coat was

84

dollars, we set up the equation

1.12x = 84

. Solving for

x

yields

x = \frac{84}{1.12} = 75

Step-by-Step Solution

Represent the retail price in terms of the wholesale price

x

Retail price =

1.40x

A markup of

40\%

x

is equivalent to multiplying

x

1 + 0.40 = 1.40

Represent the sale price in terms of the retail price.

Sale price =

0.80(1.40x) = 1.12x

A discount of

20\%

off the retail price is equivalent to multiplying the retail price by

1 - 0.20 = 0.80

Set up the equation with the given sale price and solve for

x

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

The sale price of the coat is given as

84

dollars, so we set the algebraic representation equal to

84

and solve for

x

Key Concept

Applying consecutive percentage increases and decreases to find initial values.

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