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