Naomi bought both rabbit snails and nerite snails for a total of $52. Each rabbit snail costs $8 and each...
GMAT Algebra : (Alg) Questions
Naomi bought both rabbit snails and nerite snails for a total of \(\mathrm{\$52}\). Each rabbit snail costs \(\mathrm{\$8}\) and each nerite snail costs \(\mathrm{\$6}\). If Naomi bought \(\mathrm{2}\) nerite snails, how many rabbit snails did she buy?
1. TRANSLATE the problem information
- Given information:
- Total spent on both types of snails: $52
- Cost per rabbit snail: $8
- Cost per nerite snail: $6
- Number of nerite snails bought: 2
- Need to find: number of rabbit snails
- Let \(\mathrm{x}\) = number of rabbit snails Naomi bought
2. TRANSLATE the costs into mathematical expressions
- Cost of all rabbit snails: \(\mathrm{8x}\) (since each costs $8)
- Cost of all nerite snails: \(\mathrm{6(2) = \$12}\) (since she bought 2 at $6 each)
- Total cost equation: \(\mathrm{8x + 12 = 52}\)
3. SIMPLIFY by solving the linear equation
- Start with: \(\mathrm{8x + 12 = 52}\)
- Subtract 12 from both sides: \(\mathrm{8x = 40}\)
- Divide both sides by 8: \(\mathrm{x = 5}\)
Answer: A. 5
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students often struggle to identify what the variable should represent or how to set up the total cost equation correctly.
Some students might set up the equation as \(\mathrm{8x + 6x = 52}\), thinking they need to find both types of snails, forgetting that they already know she bought exactly 2 nerite snails. Others might write \(\mathrm{8x + 6 = 52}\), forgetting to multiply the nerite snail cost by the quantity of 2.
This may lead them to select Choice C (14) or get confused and guess randomly.
Second Most Common Error:
Poor SIMPLIFY execution: Students make arithmetic mistakes when solving \(\mathrm{8x + 12 = 52}\).
A common error is:
\(\mathrm{8x + 12 = 52}\)
\(\mathrm{8x = 52 + 12}\)
\(\mathrm{8x = 64}\)
\(\mathrm{x = 8}\)
Since 8 isn't an answer choice, this leads to confusion and guessing.
The Bottom Line:
This problem tests your ability to translate a real-world situation into a mathematical equation and then solve it systematically. The key is recognizing that you already know the cost of the nerite snails ($12), so you only need one variable for the unknown rabbit snails.