Tea blend A is 30% green tea by weight, and tea blend B is... | SAT Systems of two linear equations in two variables Question, Answer Explained

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Math · AlgebraHard

Tea blend A is $30\%$ green tea by weight, and tea blend B is $80\%$ green tea by weight. How many ounces of blend A should be mixed with blend B to make $40$ ounces of a mixture that is $50\%$ green tea by weight?

$16$

$20$

$24$

$32$

Show answer and explanation

Answer: C

Let $a$ and $b$ be the numbers of ounces of blends A and B. Then $a + b = 40$ and $0.30a + 0.80b = 0.50(40) = 20$ . Substituting $b = 40 - a$ gives $0.30a + 32 - 0.80a = 20$ , so $-0.50a = -12$ and $a = 24$ .

Choice A, $16$ , is the amount of blend B, not blend A.

Why the other choices are wrong

A. 16 ounces is the amount of blend B. Blend A makes up the other 24 ounces.
B. Equal amounts of the blends would give 55% green tea, the average of 30% and 80%, not 50%.
D. 32 is the number of ounces of green tea in 40 ounces of blend B, 0.80 × 40.

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