SOLUTION: A box contains apples and pears. An equal number of apples and pears are rotten. 2/3 of the all the apples are rotten and 3/4 of all the pears are rotten. What fraction of the to

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A box contains apples and pears. An equal number of apples and pears are rotten. 2/3 of the all the apples are rotten and 3/4 of all the pears are rotten. What fraction of the to      Log On


   



Question 312901: A box contains apples and pears. An equal number of apples and pears are
rotten. 2/3 of the all the apples are rotten and 3/4 of all the pears are rotten.
What fraction of the total number of pieces of fruit in the box is rotten?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = number of apples
Let p = number of pears
given:
%282%2F3%29%2Aa+=+%283%2F4%29%2Ap
a+=+%283%2F2%29%2A%283%2F4%29%2Ap
p+=+%288%2F9%29%2Aa
%282%2F3%29%2Aa+%2F+%28a+%2B+p%29+=+%282%2F3%29%2Aa+%2F+%28a+%2B+%288%2F9%29%2Aa%29
%28%282%2F3%29%2Aa%29+%2F%28+%2817%2F9%29%2Aa%29+=+%282%2F3%29%2A%289%2F17%29
%282%2F3%29%2A%289%2F17%29+=+6%2F17
6/17 of the box are apples that are rotten
6/17 of the box are peas that are rotten
12/17 of the fruit in the box is rotten