AMC 8 1998 Problem 14

AMC8 1998 年第 14 题

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An Annville Junior High School, 30% of the students in the Math Club are in the Science Club, and 80% of the students in the Science Club are in the Math Club. There are 15 students in the Science Club. How many students are in the Math Club?
在 Annville 初中,数学俱乐部中 30% 的学生也在科学俱乐部,科学俱乐部中 80% 的学生也在数学俱乐部。科学俱乐部有 15 名学生。数学俱乐部有多少名学生?
  1. A.12
  2. B.15
  3. C.30
  4. D.36
  5. E.40

正确答案 · Correct Answer

E

解析 · Solution

Solution 1

If 80% of the people in the science club of 15 people are in the Math Club, 45×15=12\displaystyle \frac{4}{5} \times15=12 people are in the both the Math Club and the Science Club.
These 12 people make up 30% of the Math Club.
Setting up a proportion:
12⋅1.00=0.30⋅x12\cdot 1.00 =0.30\cdot x, 120.3=40=x\displaystyle \frac{12}{0.3} = 40 = x
There are 40=E people in the Math Club.

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