Examkin

Question

Difficulty: MediumPercent Change and Interest

A boutique clothing retailer purchases a line of jackets for a wholesale price of xx dollars. The retailer marks up the wholesale price by 50%50\% to set the original retail price. During a seasonal clearance sale, the original retail price is discounted by 30%30\%. If a customer purchases a jacket during the clearance sale for $126\$126, what was the original wholesale price of the jacket, xx?

  1. A
    $90\$90
  2. B
    $105\$105
  3. $120\$120Answer
  4. D
    $150\$150
  5. E
    $180\$180

Answer

The original wholesale price of the jacket is $120\$120.
The wholesale price xx is increased by 50%50\%, giving a retail price of 1.5x1.5x. A 30%30\% discount reduces this retail price to 70%70\% of its value: 1.5x×0.7=1.05x1.5x \times 0.7 = 1.05x. Given that the final price is $126\$126, solving 1.05x=1261.05x = 126 gives x=$120x = \$120.

Step-by-Step Solution

1
Express the original retail price in terms of the wholesale price xx.
Original Retail Price =x×(1+0.50)=1.50x= x \times (1 + 0.50) = 1.50x
A 50%50\% markup increases the initial value by a factor of 1.501.50.
2
Express the clearance sale price in terms of the original retail price.
Clearance Sale Price =1.50x×(1−0.30)=1.50x×0.70=1.05x= 1.50x \times (1 - 0.30) = 1.50x \times 0.70 = 1.05x
A 30%30\% discount means paying 70%70\% of the marked-up retail price.
3
Set the sale price expression equal to $126\$126 and solve for xx.
1.05x=126  ⟹  x=1261.05=12600105=1201.05x = 126 \implies x = \frac{126}{1.05} = \frac{12600}{105} = 120
Dividing the clearance sale price by the net multiplier yields the original wholesale price.

Key Concept

Successive Percent Change and Multiplier Bases
Rate this question

Topics

Percent Change and Interest

More questions from this topic