A car rental company charges customers using the formula C = 75 + 25m, where C represents the total cost...
GMAT Algebra : (Alg) Questions
A car rental company charges customers using the formula \(\mathrm{C = 75 + 25m}\), where \(\mathrm{C}\) represents the total cost in dollars and \(\mathrm{m}\) represents the number of miles driven. The $75 represents a daily rental fee. If a customer's total cost was $425, how many miles did the customer drive?
1. TRANSLATE the problem information
- Given information:
- Formula: \(\mathrm{C = 75 + 25m}\) (where \(\mathrm{C}\) = total cost, \(\mathrm{m}\) = miles driven)
- Customer's actual total cost: \(\mathrm{C = \$425}\)
- Need to find: number of miles driven (\(\mathrm{m}\))
- What this tells us: We have the formula and one known value, so we can substitute and solve.
2. INFER the approach
- Since we know \(\mathrm{C = 425}\) and have the formula \(\mathrm{C = 75 + 25m}\), we can substitute the known cost value into the equation
- Then solve for \(\mathrm{m}\) by isolating it on one side of the equation
3. SIMPLIFY by substituting and solving
- Substitute \(\mathrm{C = 425}\):
\(\mathrm{425 = 75 + 25m}\) - Subtract 75 from both sides:
\(\mathrm{425 - 75 = 25m}\) - Calculate:
\(\mathrm{350 = 25m}\) - Divide both sides by 25:
\(\mathrm{m = 350 \div 25 = 14}\)
Answer: B. 14
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students might confuse what's given versus what they need to find, potentially setting up the equation as \(\mathrm{m = 75 + 25(425)}\) or trying to solve for \(\mathrm{C}\) instead of \(\mathrm{m}\).
This confusion about the problem setup leads them to perform calculations on the wrong values, resulting in answers that don't match any of the given choices, causing them to guess randomly.
Second Most Common Error:
Poor SIMPLIFY execution: Students correctly set up \(\mathrm{425 = 75 + 25m}\) but make arithmetic errors during the calculation steps, such as incorrectly calculating \(\mathrm{425 - 75 = 250}\) instead of 350, or dividing incorrectly.
This may lead them to select Choice A (12) if they calculated \(\mathrm{300 \div 25 = 12}\) due to the subtraction error.
The Bottom Line:
This problem tests whether students can correctly identify what's known versus unknown in a linear equation context and then systematically isolate the variable through inverse operations. Success requires careful attention to both setup and calculation accuracy.