A chemist mixes x liters of a 20\% acid solution with y liters of a 50\% acid solution to … — GMAT

A chemist mixes $x$ liters of a $20\%$ acid solution with $y$ liters of a $50\%$ acid solution to produce $30$ liters of a $40\%$ acid solution. How many liters of the $20\%$ acid solution were used in the mixture?

Answer: 10 liters

Answer

10 liters of the 20% acid solution were used.

Solving the system of simultaneous linear equations

x + y = 30

and

0.20x + 0.50y = 12

yields

x = 10

liters.

Step-by-Step Solution

Formulate the linear system of equations representing total volume and total pure acid content.

x + y = 30

and

0.20x + 0.50y = 12

The sum of component volumes equals total volume, and the sum of pure acid contents equals total pure acid.

Substitute

y = 30 - x

into the pure acid equation.

0.20x + 0.50(30 - x) = 12

Reduces the two-variable system to a single linear equation in terms of

x

Expand and solve for

x

15 - 0.30x = 12 \implies -0.30x = -3 \implies x = 10

Isolates the target variable

x

representing the volume of the 20% acid solution.

Key Concept

Simultaneous Linear Equations in Mixture Problems

Estimated Time:1m 0s

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