Bill weighs 120 lbs and is gaining ten lbs each month. phil weighs 150 lbs and is gaining four lbs each month. how many months will it take for bill to wiegh the same as phil?

First, let's write two expressions, letting x= the number of months which have elapsed:

Bill: 120 + 10x
Phil: 150 + 4x

If we set them equal to each other, then solve for x, that will be the number of months where their weights equal each other:

120+10x = 150 + 4x   [starting equation]
-120  -4x    -120 -4x    [ subtract 120 from both sides, and 4x from both sides, to isolate the term with the variable]

6x = 30     [divide both sides by 5]
 5      5

x=6. They will weigh the same in six months.