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Zorluk: Çok zorPercentage Change, Markups, and Discounts

An electronics store marks up the wholesale cost of a laptop by 40% to establish its regular retail price. During a clearance event, the laptop is discounted by 25% from its regular price. A customer then uses a special promotional code that takes an additional 10% off the sale price. If the final price the customer pays before tax is $756.00, what was the original wholesale cost of the laptop?

  1. A
    $623.70
  2. B
    $720.00
  3. $800.00Cevap
  4. D
    $8,000.00

Cevap

The original wholesale cost of the laptop was $800.00.
The correct answer is found by representing the consecutive percent changes as multipliers (1.40 for a 40% markup, 0.75 for a 25% discount, and 0.90 for a 10% discount). Setting the product of these multipliers and the unknown wholesale cost equal to the final price (W×1.40×0.75×0.90=756.00W \times 1.40 \times 0.75 \times 0.90 = 756.00) yields a net multiplier of 0.945. Dividing the final price of 756.00by0.945givestheoriginalwholesalecostof756.00 by 0.945 gives the original wholesale cost of 800.00.

Adım Adım Çözüm

1
Let WW be the wholesale cost. Represent the markup of 40% as a multiplier.
Regular price = W×1.40W \times 1.40
A 40% markup means the regular price is 140% of the wholesale cost.
2
Apply the 25% clearance discount to the regular price expression.
Sale price = (W×1.40)×0.75=W×1.05(W \times 1.40) \times 0.75 = W \times 1.05
A 25% discount means the customer pays 75% of the current price.
3
Apply the 10% promotional code discount to the sale price expression.
Final price = (W×1.05)×0.90=W×0.945(W \times 1.05) \times 0.90 = W \times 0.945
An additional 10% discount means the customer pays 90% of the sale price.
4
Set the final price expression equal to the given final price and solve for WW.
W×0.945=756.00⇒W=756.000.945=800.00W \times 0.945 = 756.00 \Rightarrow W = \frac{756.00}{0.945} = 800.00
This isolates WW to find the original wholesale cost.

Anahtar Kavram

Calculating original value after successive percent changes (markups and discounts)
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Konular

Percentage Change, Markups, and Discounts

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