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Difficulty: EasyAlgebraic Word Problems and Modeling

A retailer purchases items for xx dollars each and sets the regular selling price at a 40%40\% markup above the purchase price. During a clearance event, the retailer discounts the regular selling price by 15%15\%. Which of the following statements regarding the pricing of an item must be true? Select all such statements.

  1. The regular selling price of an item is 1.40x1.40x dollars.Answer
  2. The clearance sale price of an item is 1.19x1.19x dollars.Answer
  3. C
    The clearance sale price represents a 25%25\% markup above the original purchase price xx.
  4. D
    The dollar profit earned on each item sold during the clearance event is 0.25x0.25x dollars.

Answer

The statements confirming that the regular selling price is 1.40x1.40x dollars and that the clearance sale price is 1.19x1.19x dollars are correct.
The regular selling price is computed by increasing the cost xx by 40%, yielding 1.40x1.40x. The clearance price is found by reducing 1.40x1.40x by 15%, which equals 1.40x×0.85=1.19x1.40x \times 0.85 = 1.19x. Therefore, both the statement that the regular price is 1.40x1.40x dollars and the statement that the clearance price is 1.19x1.19x dollars are correct.

Step-by-Step Solution

1
Model the regular selling price using the original purchase price xx and the 40%40\% markup.
Regular price =x×(1+0.40)=1.40x= x \times (1 + 0.40) = 1.40x.
A 40% markup increases the base cost xx by 0.40 times its original value.
2
Model the clearance sale price by applying a 15%15\% discount to the regular selling price.
Clearance price =1.40x×(1−0.15)=1.40x×0.85=1.19x= 1.40x \times (1 - 0.15) = 1.40x \times 0.85 = 1.19x.
A 15% discount reduces the regular price to 85% of its value.
3
Calculate the effective markup percentage and profit per item to evaluate all statements.
Profit =1.19x−x=0.19x= 1.19x - x = 0.19x, which is a 19%19\% net markup over the purchase price xx.
Comparing 1.19x1.19x to the base cost xx shows a net gain of 0.19x0.19x per unit.

Key Concept

Applying successive percent changes in algebraic modeling by using correct base values.
Estimated Time:1m 0s
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Topics

Algebraic Word Problems and Modeling

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