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If I give you seven apples, you will then have five times as many as I would then have, however, if you give me seven apples, we will then both have the same number of apples. How many apples do I currently have?

Answer: I have 14 apples and you have 28 apples.

We can easily work this out with a little algebra. I have A apples and you have B apples, then

5 x (A - 7) = B + 7    [1]

A + 7 = B - 7    [2]

From [1] we have:

5A - 35 = B + 7
5A = B + 42   [3]

From [2] we have:

A + 14 = B        [4]

We can then use [4] in [3] to give:

5A = (A + 14) + 42
5A = A + 56
4A = 56
A = 14

Which gives B = 28 (by [4]). QED.

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