A chemist combines water and acetic acid to make a mixture with a volume of 56 milliliters (mL). The volume...
GMAT Algebra : (Alg) Questions
A chemist combines water and acetic acid to make a mixture with a volume of 56 milliliters (mL). The volume of acetic acid in the mixture is 10 mL. What is the volume of water, in mL, in the mixture? (Assume that the volume of the mixture is the sum of the volumes of water and acetic acid before they were mixed.)
1. TRANSLATE the problem information
- Given information:
- Total mixture volume = 56 mL
- Acetic acid volume = 10 mL
- Need to find: water volume
- Total volume = water volume + acetic acid volume
- Let \(\mathrm{x}\) represent the volume of water in mL
2. TRANSLATE the relationship into an equation
- Since total volume equals water volume plus acetic acid volume:
- \(\mathrm{x + 10 = 56}\)
3. SIMPLIFY to solve for x
- Subtract 10 from both sides:
- \(\mathrm{x + 10 - 10 = 56 - 10}\)
- \(\mathrm{x = 46}\)
Answer: 46
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students might confuse which quantities to combine or misread the problem setup.
Some students might think they need to find the total volume instead of the water volume, or they might subtract when they should add. For example, they might calculate \(\mathrm{56 - 10 = 46}\) but then think this represents something other than the water volume.
This typically leads to confusion and guessing rather than selecting a specific wrong answer.
The Bottom Line:
This problem tests basic translation skills from English to mathematical equations. The key challenge is carefully reading what quantity you're asked to find and setting up the correct equation. Once the equation \(\mathrm{x + 10 = 56}\) is established, the solution is straightforward arithmetic.