Question

A positive integer is divided by a smaller positive integer. The integer part of the quotient is 9 and the remainder is 1. The sum of the two integers is 71. Find the two integers.

Answer 1

off the top of my head i would start with the two equations
\[m+n=71\] and \[\frac{m}{n}=9+\frac{1}{n}\]

Answer 2

multiply the second equation by \(n\) and get \(m=9n+1\) so really you have
\[m+n=71\]\[m=9n+1\] you can replace \(m\) in the first equation by \(9n+1\) and get
\[9n+1+n=71\] and solve that one more or less in your head