MathRevolution wrote:
[GMAT math practice question]
The 20% acid liquid solution is produced by adding a gallons of 10% acid liquid solution to b gallons of 50% acid liquid solution. To get 10 gallons of 20% acid liquid solution, how many gallons of 50% acid liquid solution are needed?
A. 1
B. 1.5
C. 2
D. 2.5
E. 3
To find the amount of one solution in a resultant mixture, I use this weighted average formula:
\((Concen_{A})(Vol_{A}) + (Concen_{B})(Vol_{B}) = (Concen_{A+B})(Vol_{A+B})\) Let A = volume of the solution with 10% acid
Let B = volume of the solution with 50% acid
A + B = resultant mixture
A + B = 10 (gallons in volume)
A = (10 - B)
Desired concentration of resultant solution: 20%
1) the equation without substitution
\((.10)(A) + (.50)(B) = .20(A + B)\)2) Substitute (10-B) for A, and 10 for (A+B):
\(.10(10-B) + .50B = .20(10)\)
\(1 - .10B + .50B = 2\)
\(.40B = 1\)
\(B =\frac{1}{.4}=\frac{10}{4}=2.5\)Answer D
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