Phill weighs 120 pounds and is gaining ten pounds each month. Phil weighs 150 pounds and is gaining 4 pounds each month. How many months, m, will it take for Bill to weigh the same as Phil?

Mathematics · High School · Tue Nov 03 2020

Answered on

Given:

Bill weighs 120 pounds and is gaining ten pounds each month. 

Phil weighs 150 pounds and is gaining 4 pounds each month

Determine how many months will it take for Bill to weigh the same as Phil.

Representation:

m = number of months

Bill

120 + 10m

Phil

150 + 4m

Solution:

In order to solve for the number of months, simply equate the two solutions in one equation.

150 + 4m = 120 + 10m

Transpose 4m and 120 on the opposite sides of the equation. Note that when transposing a number, the sign changes.

150 -120 = 10m -4m

30 = 6m

Divide both sides by 6 in order to get the value of m

m = 5

To check if they have the same weight after 5 months, we substitute the value of 5 in the equation.

Bill

120 + 10(5)

120 + 50

=170

Phil

150 + 4(5)

150 + 20

= 170

Final answer:

m = 5 or 5 months