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Zorluk: OrtaProfit, Loss, and Markup

A store owner purchased a shipment of coats. She marked up the cost price of each coat by 40%40\% to set the regular selling price. During a clearance sale, she offered a discount of 15%15\% off the regular selling price on all remaining coats. If a coat was sold at the clearance price for $238\$238, what was the cost price of the coat?

  1. A
    $168.00\$168.00
  2. B
    $170.00\$170.00
  3. C
    $190.40\$190.40
  4. $200.00\$200.00Cevap
  5. E
    $212.50\$212.50

Cevap

The cost price of the coat was $200.00\$200.00.
The correct answer is $200.00\$200.00. The regular price is 140%140\% of the cost price (1.40C1.40C). A 15%15\% discount on the regular price means the clearance price is 85%85\% of the regular price, which translates to 0.85×1.40C=1.19C0.85 \times 1.40C = 1.19C. Setting 1.19C=$2381.19C = \$238 yields C=$200.00C = \$200.00.

Adım Adım Çözüm

1
Define variables and express the regular selling price in terms of the cost price.
Let CC be the cost price of a coat. The regular selling price is R=C+0.40C=1.40CR = C + 0.40C = 1.40C.
Markup is calculated as a percentage of the cost price.
2
Express the clearance price in terms of the regular selling price and cost price.
The clearance price is R×(1−0.15)=1.40C×0.85=1.19CR \times (1 - 0.15) = 1.40C \times 0.85 = 1.19C.
The discount of 15%15\% is applied to the regular selling price, resulting in 85%85\% of the regular selling price.
3
Solve for the cost price CC using the given clearance price.
1.19C=238  ⟹  C=2381.19=2001.19C = 238 \implies C = \frac{238}{1.19} = 200.
Equating the algebraic expression for the clearance price to the given numerical value gives the original cost price.

Anahtar Kavram

Successive Percentage Changes in Profit and Loss
Bu soruyu puanla

Konular

Profit, Loss, and Markup

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