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Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

In a class of 80 seniors, there are 3 boys for every 5 girls. In the junior class, there are 3 boys for every 2 girls. If the two classes combined have an equal number of boys and girls, how many students are in the junior class?

(A) 72
(B) 80
(C) 84
(D) 100
(E) 120

答案和解析

答案：D

解析：

Among the eighty seniors, there are 3 boys for every 5 girls, so 3 over 8 of the seniors, or 30, are boys and 5 over 8, or 50, are girls. Among the juniors, 3 over 5 are boys and 2 over 5 are girls. If x stands for the total number of juniors, then (3 over 5) times x are boys and (2 over 5) times x are girls. The total number of senior and junior boys is 30 + ((3 over 5) times x). The total number of senior and junior girls is 50 + ((2 over 5) times x). The question states that these quantities are equal, so 30 + ((3 over 5) times x) = 50 + ((2 over 5) times x). Solving this gives 150 + 3 times x = 250 + 2 times x, or x = 100.