Let's represent Jeff's weight as an equation and Darius' weight as an equation where [tex]m[/tex] equals the number of months they have been gaining/losing pounds.
Jeff's weight can be modeled by the equation below:
[tex]J = 120 + 10m[/tex]
Darius' weight can be modeled by the equation below:
[tex]D = 150 + 4m[/tex]
Since we are trying to find when the weights will be equal, let's set the equations equal to each other and solve:
[tex]120 + 10m = 150 + 4m[/tex]
- Set equations equal to each other
[tex]120 + 6m = 150[/tex]
- Subtract [tex]4m[/tex] from both sides
[tex]6m = 30[/tex]
- Subtract 120 from both sides of the equation
[tex]m = 5[/tex]
- Divide both sides of the equation by 6
We have found m = 5. This means that the number of months it will take for their weights to be equal is 5.
