Apples, oranges, bananas and pears

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Subject: Math/Weights
Name: Richard
Who are you: Other

If 6 oranges weights as much as 4 apples, 5 bananas weights as much as 3 pears, and ten bananas weights as much as 8 oranges. How many pears and apples would you need to have their weights balanced.

Richard,

I would start by constructing a table of fruit that balance.

6 oranges	balance with	4 apples
5 bananas	balance with	3 pears
10 bananas	balance with	8 oranges

What I see is that 5 bananas balance with 3 pears so 10 bananas balance with 6 pears, so I can add another line

6 oranges	balance with	4 apples
5 bananas	balance with	3 pears
10 bananas	balance with	8 oranges
10 bananas	balance with	6 pears

Thus 8 oranges balance with 6 pears.

6 oranges	balance with	4 apples
5 bananas	balance with	3 pears
10 bananas	balance with	8 oranges
10 bananas	balance with	6 pears
8 oranges	balance with	6 pears

We don't need the banana rows now so I can reduce the table to

6 oranges	balance with	4 apples
8 oranges	balance with	6 pears

I can now reduce each row by dividing by 2

3 oranges	balance with	2 apples
4 oranges	balance with	3 pears

Can yo see how to proceed,
Penny

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