A printing service charges $0.15 per page for document copying. Which function C models the total cost in dollars for...
GMAT Algebra : (Alg) Questions
A printing service charges \(\$0.15\) per page for document copying. Which function C models the total cost in dollars for copying x pages at this rate?
- \(\mathrm{C(x) = \frac{x}{0.15}}\)
- \(\mathrm{C(x) = x + 0.15}\)
- \(\mathrm{C(x) = x - 0.15}\)
- \(\mathrm{C(x) = 0.15x}\)
1. TRANSLATE the problem information
- Given information:
- Cost per page = \(\$0.15\)
- Number of pages = \(\mathrm{x}\)
- Need to find function \(\mathrm{C(x)}\) for total cost
- This tells us we need to find how total cost depends on the number of pages.
2. INFER the mathematical relationship
- When you have a cost "per item," total cost is always:
Total Cost = (Cost per item) × (Number of items) - Here: \(\mathrm{Total\;Cost = (\$0.15\;per\;page) \times (x\;pages) = 0.15x}\)
3. Write the function
- Therefore: \(\mathrm{C(x) = 0.15x}\)
- Check: For 10 pages, cost would be \(\mathrm{C(10) = 0.15(10) = \$1.50}\) ✓
Answer: D
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students misinterpret what "per page" means mathematically and get confused about which operation to use.
Some students think "per" means division and create \(\mathrm{C(x) = x/0.15}\), believing they should divide the number of pages by the cost. Others think they should simply add the cost to the number of pages, creating \(\mathrm{C(x) = x + 0.15}\). This confusion about the mathematical meaning of "per unit" cost leads them to select Choice A \(\mathrm{(x/0.15)}\) or Choice B \(\mathrm{(x + 0.15)}\).
The Bottom Line:
The key insight is recognizing that "per page" indicates a multiplication relationship: total cost equals the rate per page times the number of pages. Once you translate this correctly, the math becomes straightforward.