During a fundraising event, a nonprofit organization collected a total of $1,472 from selling t-shirts for a hours and hoodies...
GMAT Algebra : (Alg) Questions
During a fundraising event, a nonprofit organization collected a total of $1,472 from selling t-shirts for a hours and hoodies for b hours. The equation \(42\mathrm{a} + 56\mathrm{b} = 1,472\) represents this situation. Which of the following is the best interpretation of 56 in this context?
Choose 1 answer:
- The organization sold hoodies for $56 per hour during the event.
- The organization worked 56 hours selling t-shirts during the event.
- The organization sold t-shirts for $56 per hour during the event.
- The organization worked 56 hours selling hoodies during the event.
The organization sold hoodies for $56 per hour during the event.
The organization worked 56 hours selling t-shirts during the event.
The organization sold t-shirts for $56 per hour during the event.
The organization worked 56 hours selling hoodies during the event.
1. TRANSLATE the equation components
- Given equation: \(42\mathrm{a} + 56\mathrm{b} = 1,472\)
- Given context information:
- a = hours selling t-shirts
- b = hours selling hoodies
- Total collected = $1,472
2. INFER the meaning of each coefficient
- In linear equations like this, we have the structure: \(\text{rate} \times \text{time} + \text{rate} \times \text{time} = \text{total}\)
- Since a represents time (hours selling t-shirts), the coefficient 42 must be the rate per hour for t-shirts
- Since b represents time (hours selling hoodies), the coefficient 56 must be the rate per hour for hoodies
3. TRANSLATE back to context
- The coefficient 56 multiplies b (hours selling hoodies)
- Therefore, 56 represents dollars collected per hour from selling hoodies
- This means: $56 per hour selling hoodies
Answer: A) The organization sold hoodies for $56 per hour during the event.
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skills: Students confuse what the coefficient represents versus what the variable represents.
They might think "56 is just a number in the equation" without connecting it to the rate structure. Some students see 56 and think it represents the actual hours worked rather than the rate per hour. This leads them to select Choice D (The organization worked 56 hours selling hoodies).
Second Most Common Error:
Poor INFER reasoning: Students don't recognize the rate × time structure of linear equations in context.
They might randomly associate 56 with t-shirts instead of hoodies, not understanding that coefficients pair with their respective variables. This confusion may lead them to select Choice C (The organization sold t-shirts for $56 per hour).
The Bottom Line:
This problem tests whether students can connect abstract equation structure to real-world meaning. The key insight is recognizing that coefficients in rate equations represent "per unit" values.
The organization sold hoodies for $56 per hour during the event.
The organization worked 56 hours selling t-shirts during the event.
The organization sold t-shirts for $56 per hour during the event.
The organization worked 56 hours selling hoodies during the event.