A box contains apples and pears. An equal number of apples and pears are rotten. 2/3 of all the apples are rotten. 3/4 of all the pears are rotten. What fraction of the fruit in the box is rotten?
+2 Answer: 12/17 of the fruit is rotten
Let a=# of apples and p=# of pears.
(2/3)*a=(3/4)*p
so
a=(3/2)*(3/4)*p
p=(8/9)*a
The total amount of rotten fruit is: 2*(2/3)*a=(4/3)*a
The total fruit in box is: a+p=a+(8/9)*a=(9/9)*a+(8/9)*a=(17/9)*a
so the fraction of the fruit rotten is: (4/3)/(17/9)
simplifying it, we get 12/17
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