2002 AMC 8 Problems/Problem 24

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?

$\text{(A)}\ 30\qquad\text{(B)}\ 40\qquad\text{(C)}\ 50\qquad\text{(D)}\ 60\qquad\text{(E)}\ 70$

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

\[\frac{8/3}{8/3+4} \times 100 = \frac{8}{8+12} \times 100  = \boxed{\text{(B)}\ 40}\]

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 $6$, 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 $16/(16+24)=16/40$. Simplifying, we get $2/5$. Hence the answer is $\boxed{\text{(B)}\ 40}$.

Video Solution

https://youtu.be/KqOE0AvrRs8 Soo, DRMS, NM

See Also

2002 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 23
Followed by
Problem 25
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All AJHSME/AMC 8 Problems and Solutions

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