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Zorluk: OrtaPercent 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\$120Cevap
  4. D
    $150\$150
  5. E
    $180\$180

Cevap

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.

Adım Adım Çözüm

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.

Anahtar Kavram

Successive Percent Change and Multiplier Bases
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Konular

Percent Change and Interest

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