AMC 8 2010 Problem 15
AMC8 2010 年第 15 题
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A jar contains 5 different colors of gumdrops. 30% are blue, 20% are brown, 15% are red, 10% are yellow, and other 30 gumdrops are green. If half of the blue gumdrops are replaced with brown gumdrops, how many gumdrops will be brown?
一个罐子装有 5 种不同颜色的口香糖：30％是蓝色的，20％是棕色的，15％是红色的，10％ 是黄色的，且其他 30 个口香糖是绿色的。若蓝色口香糖的一半被棕色口香糖代替，那么有多少个口香糖将是棕色的？
- A.35
- B.36
- C.42
- D.48
- E.64
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
We do 100-30-20-15-10 to find the percent of gumdrops that are green. We find that 25% of the gumdrops are green. That means there are 120 gumdrops. If we replace half of the blue gumdrops with brown gumdrops, then 15% of the jar's gumdrops are brown.
We first calculate the percentage of gumdrops that are green. Subtracting all the other percentages from 100 %, we have: 100-30-20-15-10 = 25%. Thus, 25% of the gumdrops are green. Next, we set up a proportion: 30 25 % = 𝑥 30 % to find the number of blue gumdrops. Cross-multiplying, we solve for 𝑥: 36 So there are 36 blue gumdrops. We divide the number of blue gumdrops by 2 to get 18 Now, we calculate the number of brown marbles using the proportion: 30 25 % = 𝑦 20 %, where 𝑦 is the number of brown marbles. Solving, we find y = 24. Adding these together gives: 24 + 18 = 42. Thus, the answer is 42
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