SOLUTION: Hi There were 108 fruits in a box. Bob gave away 3/8 of the oranges 1/3 of the pears and doubled the number of apples in the box. He then had an equal number of oranges pears and

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Hi There were 108 fruits in a box. Bob gave away 3/8 of the oranges 1/3 of the pears and doubled the number of apples in the box. He then had an equal number of oranges pears and       Log On

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Question 1193370: Hi
There were 108 fruits in a box. Bob gave away 3/8 of the oranges 1/3 of the pears and doubled the number of apples in the box. He then had an equal number of oranges pears and apples left in the box. How many apples did he add.
Thanks
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
n oranges
p peas
a apples

n%2Bp%2Ba=108


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Bob gave away 3/8 of the oranges 1/3 of the pears and doubled the number of apples in the box.
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Expressions for each becomes
5n%2F8 oranges
2p%2F3 pears
2a apples

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He then had an equal number of oranges pears and apples left in the box.
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.
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You can continue,...

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


o = original number of oranges
p = original number of pears
a = original number of apples

The original number of fruits was 108:

o%2Bp%2Ba+=+108 [1]

After he gave away 3/8 of the oranges and 1/3 of the pears and doubled the number of apples, the numbers of the different fruits were

oranges: (5/8)o
pears: (2/3)p
apples: 2a

The numbers of fruits were now all the same:

%285%2F8%29o+=+%282%2F3%29p+=+2a [2]

Use [2] to express the numbers of all three types of fruit using a single variable...

%285%2F8%29o=2a
o=%288%2F5%29%282a%29=%2816%2F5%29a

%282%2F3%29p=2a
p=%283%2F2%29%282a%29=3a

... and substitute in [1] to solve the problem.

%2816%2F5%29a%2B3a%2Ba=108
%2836%2F5%29a=108
a=%285%2F36%29108=5%283%29=15

CHECK:
original number of apples = a = 15
original number of pears = 3a = 45
original number of oranges = (16/5)a=48
15+45+48=108

He started with a=15 apples and finished with 2a=30 apples; the number of apples he added was 15.

ANSWER: He added 15 apples