Possible percent problem

Algebra Level 3

Consider numbers aa and bb such that ab=24%\frac{a}{b}=24\% when rounded to the nearest whole percent.

bb could be 63 since if a=15a=15 we would have 1563.2381\frac{15}{63}\approx .2381 which rounds to 24%24\%

bb could not be 10 however since no fraction of the form a10\frac{a}{10} rounds to 24%24\%

Let x=x= the least possible value of bb for which there is a value of aa that makes ab=24%\frac{a}{b}=24\% when rounded to the nearest whole percent.

Let y=y= the greatest possible value of bb for which there is no value of aa that makes ab=24%\frac{a}{b}=24\% when rounded to the nearest whole percent.

Give the value of x+yx+y.

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