2002 AMC 8 Problems/Problem 24
Contents
[hide]Problem
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?
Solution 1
A pear gives ounces of juice per pear. An orange gives 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
Solution 2
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 , because it's the LCM of and . Then for the pears, there are ounces of pear juice. For the 6 oranges, there are ounces of orange juice. Since we are looking for the percent of pear juice, we need to do . Simplifying, we get . Hence the answer is .
Video Solution
https://www.youtube.com/watch?v=TarSWoN3ne4 ~David
See Also
2002 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.