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Difficulty: MediumDiscounts and Sale Prices

A local hardware store is purchasing a bulk wholesale order of industrial shelving. The distributor offers a 20%20\% volume discount on the order. Because the hardware store pays the invoice in full within 10 days, they receive an additional 5%5\% discount on the reduced price. If the hardware store pays $3,420\$3,420 for the shelving (before shipping and taxes), what was the original price of the bulk order?

  1. A
    $3,445\$3,445
  2. B
    $4,275\$4,275
  3. $4,500\$4,500Answer
  4. D
    $4,560\$4,560

Answer

$4,500\$4,500
The correct answer is found by representing the unknown original price as a variable, applying the 20% discount (multiplying by 0.80), and then applying the 5% discount to that new amount (multiplying by 0.95). Setting the resulting expression (0.76 times the original price) equal to the final price of 3,420anddividingyieldsanoriginalpriceof3,420 and dividing yields an original price of 4,500.

Step-by-Step Solution

1
Set up an equation representing the first discount.
Let the original price be PP. A 20%20\% discount means the price becomes 100%−20%=80%100\% - 20\% = 80\% of the original price, or 0.80P0.80P.
The volume discount is applied to the starting original price.
2
Apply the second successive discount to the result of the first.
An additional 5%5\% discount on the reduced price means the hardware store pays 100%−5%=95%100\% - 5\% = 95\% of that reduced price. This gives 0.95×0.80P=0.76P0.95 \times 0.80P = 0.76P.
Successive discounts are calculated based on the new, already-discounted price, not the original price.
3
Solve for the original price PP.
Set the expression equal to the final paid amount: 0.76P=34200.76P = 3420. Divide both sides by 0.760.76 to find P=$4,500P = \$4,500.
This isolates PP to determine the starting value before any discounts were applied.

Key Concept

Calculating the original price after successive discounts by working backward using algebraic representation.
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Topics

Discounts and Sale Prices

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