A truck can haul a maximum weight of 5,630 pounds. During one trip, the truck will be used to haul...
GMAT Algebra : (Alg) Questions
A truck can haul a maximum weight of \(\mathrm{5,630}\) pounds. During one trip, the truck will be used to haul a \(\mathrm{190}\)-pound piece of equipment as well as several crates. Some of these crates weigh \(\mathrm{25}\) pounds each and the others weigh \(\mathrm{62}\) pounds each. Which inequality represents the possible combinations of the number of \(\mathrm{25}\)-pound crates, \(\mathrm{x}\), and the number of \(\mathrm{62}\)-pound crates, \(\mathrm{y}\), the truck can haul during one trip if only the piece of equipment and the crates are being hauled?
\(25\mathrm{x} + 62\mathrm{y} \leq 5,440\)
\(25\mathrm{x} + 62\mathrm{y} \geq 5,440\)
\(62\mathrm{x} + 25\mathrm{y} \leq 5,630\)
\(62\mathrm{x} + 25\mathrm{y} \geq 5,630\)
1. TRANSLATE the problem information
- Given information:
- Truck maximum capacity: 5,630 pounds
- Equipment weight: 190 pounds (fixed load)
- Variable loads: x crates weighing 25 pounds each, y crates weighing 62 pounds each
- Need: inequality for possible combinations of x and y
2. INFER the capacity constraint
- The equipment takes up 190 pounds of the 5,630 total capacity
- Available capacity for crates = \(5,630 - 190 = 5,440\) pounds
- The crates cannot exceed this remaining capacity
3. TRANSLATE crate weights into mathematical expression
- Weight of 25-pound crates: \(25x\)
- Weight of 62-pound crates: \(62y\)
- Total crate weight: \(25x + 62y\)
4. INFER the inequality relationship
- Since total crate weight cannot exceed available capacity:
- \(25x + 62y \leq 5,440\)
Answer: A. \(25x + 62y \leq 5,440\)
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Mixing up variable assignments with crate weights
Students might incorrectly assign x to 62-pound crates and y to 25-pound crates, creating the expression \(62x + 25y\) instead of \(25x + 62y\). When combined with other errors (like forgetting to subtract equipment weight), this leads them to select Choice C (\(62x + 25y \leq 5,630\)) or Choice D (\(62x + 25y \geq 5,630\)).
Second Most Common Error:
Poor INFER reasoning: Not recognizing that equipment weight reduces available capacity
Students might think the full 5,630 pounds is available for crates, ignoring that the 190-pound equipment must also be carried. This causes them to set up \(25x + 62y \leq 5,630\) instead of the correct inequality, leading to confusion since this exact form isn't among the choices, causing them to guess.
The Bottom Line:
This problem tests whether students can systematically translate constraints while recognizing that multiple items share the same weight limit. Success requires careful variable tracking and logical reasoning about capacity allocation.
\(25\mathrm{x} + 62\mathrm{y} \leq 5,440\)
\(25\mathrm{x} + 62\mathrm{y} \geq 5,440\)
\(62\mathrm{x} + 25\mathrm{y} \leq 5,630\)
\(62\mathrm{x} + 25\mathrm{y} \geq 5,630\)