A restaurant owner plans to purchase 90 identical dinner plates from a wholesale supplier. The supplier offers a 15% volume...
GMAT Algebra : (Alg) Questions
A restaurant owner plans to purchase \(90\) identical dinner plates from a wholesale supplier. The supplier offers a \(15\%\) volume discount off the total order for purchases of \(75\) or more items. After receiving this volume discount, the restaurant owner paid exactly \(\$2,295\) for the plates. Which of the following is closest to the original price per plate before the volume discount was applied?
- \(\$27.00\)
- \(\$29.50\)
- \(\$30.00\)
- \(\$31.75\)
1. TRANSLATE the problem information
- Given information:
- 90 identical dinner plates purchased
- 15% volume discount applied
- After discount, paid exactly $2,295
- Need to find original price per plate
2. INFER the mathematical relationship
- A 15% discount means the customer pays 85% of the original price \(100\% - 15\% = 85\%\)
- If \(\mathrm{x}\) = original price per plate, then total original cost = \(90\mathrm{x}\)
- After 15% discount: \(90\mathrm{x} \times 0.85 = \$2,295\)
3. SIMPLIFY the equation to solve for x
- Set up: \(90\mathrm{x} \times 0.85 = \$2,295\)
- Calculate: \(90 \times 0.85 = 76.5\)
- So: \(76.5\mathrm{x} = \$2,295\)
- Divide both sides: \(\mathrm{x} = \$2,295 \div 76.5\) (use calculator)
- Result: \(\mathrm{x} = \$30.00\)
4. Verify the answer
- Original total cost: \(90 \times \$30.00 = \$2,700\)
- After 15% discount: \(\$2,700 \times 0.85 = \$2,295\) ✓
Answer: C ($30.00)
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students incorrectly interpret "15% discount" to mean they should multiply the final amount by 0.15 instead of recognizing that the final amount represents 85% of the original price.
They might set up: \(90\mathrm{x} = \$2,295 + (\$2,295 \times 0.15)\), leading to \(\mathrm{x} \approx \$29.50\).
This may lead them to select Choice B ($29.50).
Second Most Common Error:
Poor SIMPLIFY execution: Students set up the correct equation but make arithmetic errors when dividing $2,295 by 76.5, or they forget to divide by 90 after finding the total original cost.
If they calculate total original cost correctly as $2,700 but forget the final division by 90, they might be confused by the large number and guess randomly among the choices.
The Bottom Line:
This problem requires students to work backwards from a discounted price to find the original price, which is conceptually more challenging than calculating a discount from an original price. The key insight is recognizing that the amount paid represents 85% of the original total cost.