# A Wordy Sum!

**Algebra**Level 4

Here goes this aptly titled problem-

Half of five multiplied a large number of times by itself gives a thousand.

So does a thousandth of twenty-five when the same is done to it.

Let the number of the times the multiplication happens be denoted with \(x\) for the former and \(y\) for the latter.

Find the value of \(\frac{1}{x}-\frac{1}{y}\).

If this can be expressed as \(\frac{a}{b}\) where "a" and "b" are coprime integers...find \(a+b\)

Note- A number can be multiplied by itself even by a non-integral number of times

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