Algebra problem with two unknowns and given sum of numbers, quotient of numbers and remainder

Question

The sum of m and n is 1088.  m/n leaves a quotient 11 and a remainder of 32.  What is the value of m and n?

Answer 1

Put what the problem tells you into equation form:

(1)  m + n = 1088

(2) m/n = 11 32/n

solving (2) for m:

   m = 11n + 32

 

Substitute that in (1) and solve for n:

   11n + 32 + n = 1088

   12n = 1056

   n = 88

Solving for m:

   m + n = 1088

   m = 1088 - 88

   m = 1000