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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?

 Jun 13, 2020
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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

 

🐼

 Jun 13, 2020

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