A local hardware store is purchasing a bulk wholesale order of industrial shelving. The di… — Armed Services Vocational Aptitude Battery (ASVAB)

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

A
$\$3,445$
B
$\$4,275$
$\$4,500$ Cevap
D
$\$4,560$

Cevap

\$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

3,420 and dividing yields an original price of

4,500.

Adım Adım Çözüm

Set up an equation representing the first discount.

Let the original price be

P

. A

20\%

discount means the price becomes

100\% - 20\% = 80\%

of the original price, or

0.80P

The volume discount is applied to the starting original price.

Apply the second successive discount to the result of the first.

An additional

5\%

discount on the reduced price means the hardware store pays

100\% - 5\% = 95\%

of that reduced price. This gives

0.95 \times 0.80P = 0.76P

Successive discounts are calculated based on the new, already-discounted price, not the original price.

Solve for the original price

P

Set the expression equal to the final paid amount:

0.76P = 3420

. Divide both sides by

0.76

to find

P = \$4,500

This isolates

P

to determine the starting value before any discounts were applied.

Anahtar Kavram

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

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

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