# 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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