Your next math test is worth 111 points and contains 32 problems. each problem is worth either 4 points or 3 points. how many 3 point problems are on the test?

We call x the 4 points-worth problems and y the 3 points-worth problems

You know that x+y = 32

4x+3y = 111

You know that the difference from the x and y is 32 so write:

x = 32-y

Substitute at x the value of 32-y

4(32-y)+3y = 111

128-4y +3y = 111

-4y+3y = 111-128

-y = -17

y = 17