Difference between revisions of "2002 AMC 8 Problems/Problem 24"
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| + | ==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? | 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? | ||
<math> \text{(A)}\ 30\qquad\text{(B)}\ 40\qquad\text{(C)}\ 50\qquad\text{(D)}\ 60\qquad\text{(E)}\ 70 </math> | <math> \text{(A)}\ 30\qquad\text{(B)}\ 40\qquad\text{(C)}\ 50\qquad\text{(D)}\ 60\qquad\text{(E)}\ 70 </math> | ||
| + | |||
| + | ==Solution== | ||
| + | A pear gives <math>8/3</math> ounces of juice per pear. An orange gives <math>8/2=4</math> 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 | ||
| + | |||
| + | <cmath>\frac{8/3}{8/3+4} \times 100 = \frac{8}{8+12} \times 100 = \boxed{\text{(B)}\ 40}</cmath> | ||
| + | |||
| + | ==See Also== | ||
| + | {{AMC8 box|year=2002|num-b=23|num-a=25}} | ||
Revision as of 19:32, 23 December 2012
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
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
![\[\frac{8/3}{8/3+4} \times 100 = \frac{8}{8+12} \times 100 = \boxed{\text{(B)}\ 40}\]](http://latex.artofproblemsolving.com/4/5/9/45978beb64182b3338319ac23975cd8e57986031.png)
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 | ||
