AMC 8 2002 Problem 24
AMC8 2002 年第 24 题
比与比例★★★☆☆
Miki has a dozen oranges of the same size and a dozen pears of the same size. Miki uses her juicer to extract 8 ounces of pear juice from 3 pears and 8 ounces of orange juice from 2 oranges. She makes a pear-orange juice blend from an equal number of pears and oranges. What percent of the blend is pear juice?
Miki 有一打同样大小的桔子和一打同样大小的梨。Miki 用榨汁机能从 3 个梨中榨取 8 盎司梨汁，并且从 2 个橙子中能榨取 8 盎司橙汁。她用同样数量的梨和橙子做成了梨橙混合汁。那么这个混合汁里有百分之多少是梨汁？
- A.30
- B.40
- C.50
- D.60
- E.70
正确答案 · Correct Answer
B
解析 · Solution
Solution 1
A pear gives $8/3$ ounces of juice per pear. An orange gives 8/2 = 4 ounces of juice per orange. If the pear-orange juice blend used one pear and one orange each, the percentage of pear juice would be
Since it doesn't matter how many pears and oranges there are, you can make the number of them whatever you like. In this case, we could use 6, because it's the LCM of 2 and 3. Then for the 6 pears, there are 6/3*8=16 ounces of pear juice. For the 6 oranges, there are 6/2*8=24 ounces of orange juice. Since we are looking for the percent of pear juice, we need to do . Simplifying, we get $2/5$. Hence the answer is .
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