The total cost, C, in dollars, for a service is determined by the number of hours, h, the service is...
GMAT Algebra : (Alg) Questions
The total cost, \(\mathrm{C}\), in dollars, for a service is determined by the number of hours, \(\mathrm{h}\), the service is provided. The relationship is represented by the function \(\mathrm{C(h) = 25h}\). A customer paid a total of \(\$200\). For how many hours was the service provided?
1. TRANSLATE the problem information
- Given information:
- Cost function: \(\mathrm{C(h) = 25h}\)
- Customer's total payment: \(\$200\)
- Need to find: hours of service (h)
- What this tells us: Since the customer paid \(\$200\), we know \(\mathrm{C(h) = 200}\)
2. TRANSLATE this into a solvable equation
- Substitute the known cost into the function:
- \(\mathrm{C(h) = 25h}\)
- \(\mathrm{200 = 25h}\)
- Or equivalently: \(\mathrm{25h = 200}\)
3. SIMPLIFY by solving for h
- To isolate h, divide both sides by 25:
- \(\mathrm{25h \div 25 = 200 \div 25}\)
- \(\mathrm{h = 8}\)
Answer: 8 hours
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students may misunderstand what information to substitute into the function. They might try to solve for C instead of h, or incorrectly set up the equation as \(\mathrm{h = 25(200)}\) instead of \(\mathrm{25h = 200}\).
This confusion about which variable to solve for leads them to make calculation errors or get stuck entirely, resulting in guessing.
The Bottom Line:
This problem tests whether students can correctly identify what they know (the total cost) and what they need to find (the hours), then translate that understanding into the proper equation setup. The algebra itself is straightforward once the equation is correctly established.