Algebra word problem

Question

Two gears have a total of 80 teeth and one gear has 48 fewer teeth than the other. How many teeth does each gear have?

Answer 1

Let g be the number of teeth on the gear that has the greater number of teeth.

Then the number of teeth on the other gear is g-48.

If these two gears have a total of 80 teeth, then we have the makings of an equation:

80 = g + (g-48)

Solving,

80 = 2g + 48

32 = 2g

g = 16, and so g-48 = -32

Remember, physically realizable gears have numbers of teeth that are positive, so a negative answer for either gear means that there is no solution to this problem!