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