SOLUTION: The monthly salaries of two men are in the ratio 3:2 and their expenditures are in the ratio 8:5. Each man saves sh.500 every month. Find their monthly salaries.

From the problem, their salaries     are 3x and 2x, where x is some common measure (now unknown).

                  Their expenditures are 8y and 5y, where y is some common measure (now unknown).


Write equations as you read the problem

    3x - 8y = 500     (1)

    2x - 5y = 500     (2)


Solve equations using the Elimination method. 
For it, multiply equation (1) by 2; multiply equation (2) by 3.  You will get

    6x - 16y = 1000    (1)

    6x - 15y = 1500    (2)


Now subtract equaion (1) from equation (2).  You will get

           y = 500.


Next, from equation ((1) you get

    3x - 8*500 = 500,  3x = 500 + 4000 = 4500,  x = 4500/3 = 1500.


Thus the salary of the first man is 3x = 3*1500 = 4500;  the salary of the second man is 2x = 2*1500 = 3000.