Question

If Mary and Tom put their money together they have £36. If Mary's money were halved and Tom's money doubled they would have £42. How much does each of them have? If you're answering, could you please show working out, thanks so much.

Answer 1

Mary has £20 and Tom has £16

Explanation:

Represent their current respective money amounts by m and t.

Then m + t = £36, but also m/2 + 2t = £42.

Multiplying the second equation by 2 removes the fraction:

m + 4t = £84

and multiplying this by -1 results in

-m - 4t = -£84, which can now be added to the first equation m + t = £36:

-m - 4t = -£84

+m + t = £36

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-3t = -£48

We have successfully eliminated m. To solve this last result for t, divide both sides by -3, obtaining t = £16

Since m + t = £36 and t = £16, m must be £20.

Mary has £20 and Tom has £16