AMC 8 2020 Problem 15
AMC8 2020 年第 15 题
百分比★★★☆☆
Suppose 15% of equals 20% of $y.$ What percentage of is $y?$
假设 x 的 15％等于 y 的 20％．那么 x 的百分之几是 y?
- A.5
- B.35
- C.75
- D.
- E.300
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
Since , multiplying the given condition by 5 shows that is percent of .
Letting x=100 (without loss of generality), the condition becomes . It follows that is 75% of , so the answer is 75.
We have and , so . Solving for , we multiply by 5 to give , so the answer is 75.
We are given 0.15x = 0.20y, so we may assume without loss of generality that x=20 and y=15. This means = = , and thus the answer is 75.
15% of is $0.15x$, and 20% of is $0.20y$. We put these into an equation, 0.15x = 0.20y. Solving for by dividing 0.2 from both sides, we get , so the answer is 75.
15% of can be written as , or . 20% of can similarly be written as , or . So now, . Using cross-multiplication, we can simplify the equation as: 1500x = 2000y. Dividing both sides by 500, we get: 3x = 4y. is the same thing as 75%, so the answer is 75.
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