Lorenzo purchased a box of cereal and some strawberries at the grocery store. Lorenzo paid $2 for the box of...
GMAT Algebra : (Alg) Questions
Lorenzo purchased a box of cereal and some strawberries at the grocery store. Lorenzo paid \(\$2\) for the box of cereal and \(\$1.90\) per pound for the strawberries. If Lorenzo paid a total of \(\$9.60\) for the box of cereal and the strawberries, which of the following equations can be used to find \(\mathrm{p}\), the number of pounds of strawberries Lorenzo purchased? (Assume there is no sales tax.)
1. TRANSLATE the problem information
- Given information:
- Cereal costs \(\$2\) (fixed amount)
- Strawberries cost \(\$1.90\) per pound
- Total spent is \(\$9.60\)
- \(\mathrm{p}\) = number of pounds of strawberries purchased
- What this tells us: We need an equation that represents total cost as the sum of cereal cost plus strawberry cost.
2. TRANSLATE each cost component into mathematical expressions
- Cereal cost: \(\$2\) (this stays as 2)
- Strawberry cost: \(\$1.90\) per pound × \(\mathrm{p}\) pounds = \(1.90\mathrm{p}\)
- Total cost: \(\$9.60\)
3. INFER the equation structure
- Since total cost = cereal cost + strawberry cost
- We can write: \(1.90\mathrm{p} + 2 = 9.60\)
- This matches the structure where variable costs plus fixed costs equal total cost
Answer: A. \(1.90\mathrm{p} + 2 = 9.60\)
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students confuse which operation to use between the costs, thinking they should subtract the cereal cost from the total instead of adding it to the strawberry cost.
Their reasoning: "I need to find how much was spent on strawberries, so I subtract the cereal cost from the total." This leads them to write \(1.90\mathrm{p} - 2 = 9.60\), thinking the strawberry cost minus cereal cost equals total cost.
This may lead them to select Choice B (\(1.90\mathrm{p} - 2 = 9.60\)).
Second Most Common Error:
Poor TRANSLATE reasoning: Students mix up which value represents the rate and which represents the quantity, incorrectly thinking the \(\$2\) is multiplied by \(\mathrm{p}\) instead of \(\$1.90\).
Their reasoning: "The \(\$2\) must be the per-pound cost and \(\$1.90\) must be something else." This fundamental misreading of the problem structure leads them to set up \(1.90 + 2\mathrm{p} = 9.60\).
This may lead them to select Choice C (\(1.90 + 2\mathrm{p} = 9.60\)).
The Bottom Line:
This problem requires careful translation of real-world costs into algebraic expressions. Students must distinguish between fixed costs (cereal = \(\$2\)) and variable costs (strawberries = \(\$1.90\) × pounds) and recognize that these costs are added together, not subtracted from each other.