SAT Linear equations in one variable Practice Question 18 (Hard)

Question bank / Linear equations in one variable

Math · AlgebraHard

A chemist mixes $x$ liters of a $20\%$ acid solution with $12$ liters of a $50\%$ acid solution. The resulting mixture is a $30\%$ acid solution. What is the value of $x$ ?

$6$

$24$

$36$

$60$

Show answer and explanation

Answer: B

The acid amounts add: $0.20x + 0.50(12) = 0.30(x + 12)$ . Simplify: $0.20x + 6 = 0.30x + 3.6$ . Subtract: $2.4 = 0.10x$ , so $x = 24$ .

Choice D comes from writing the mixture's acid as $0.30x$ instead of $0.30(x + 12)$ , forgetting the 12 liters are part of the mixture.

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