Official Guide Explanation:
Problem Solving #223




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Solution and Metadata

Question: 223
Page: 184
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Ratio and Proportion >
Category 2: Word Problems > Mixture Problems >
Category 3: Arithmetic > Percents > other

Explanation: Given that we're interested in what weights of the two mixtures produce a certain amount of ryegrass, we can forget about the other quantities: the 60 percent bluegrass in X and the 75 percent fescue in Y. Instead, we can look at this like a weighted average question as follows:

((40(x) + 25(1 - x))/1) = 30. The weights are x and 1 - x because the sum of the weights should be 1, or 100%. To solve:

40(x) + 25(1 - x) = 30

40x + 25 - 25x = 30

15x = 5

x = (1/3) = 33(1/3)%. x represents the percent associated with mixture X, which is what we're looking for, so the correct choice is (B).

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