What number should you subtract from the numerator of the fraction 52,367/47,633 and add to the denominator so that, after reducing, you get 17/83?

Given fraction is [tex] \frac{52367}{47633} [/tex]Let number "x" is subtracted from numerator and added to the denominator to give new fraction [tex] \frac{17}{83} [/tex].Then we get equation:
[tex] \frac{52367-x}{47633+x}=\frac{17}{83} [/tex]Now we just need to solve this equation for xCross multiply83(52367-x)=17(47633+x)83*52367-83x=17*47633+17x4346461-83x=809761 +17x4346461-809761=83x +17x3536700=100x35367=x
Hence the required number is 35367.