### Home > AC > Chapter 5 > Lesson 5.2.1 > Problem5-68

5-68.

GETTING IN SHAPE

Frank weighs $160$ pounds and is on a diet to gain two pounds a week so that he can make the football team. John weighs $208$ pounds and is on a diet to lose three pounds a week so that he can be on the wrestling team in a lower weight class.  5-68 HW eTool (Desmos)

1. If Frank and John can meet these goals with their diets, when will they weigh the same, and how much will they weigh at that time?

Use the information in the problem to set up
$y=mx+b$ equations for both Frank and John.

Set the equations equal to each other and solve for $x$.

Substitute $x$ back into one of the original equations and solve for $y$. Check that $x$ and $y$ work in both equations.

$y=$ total weight (lbs)
$x=$ time (weeks)
$m=$ weight growth each week (lbs/week)
$b=$ starting weight (lbs)

Use the eTool below to solve the problem by completing tables and graphing.
Click on the link at right for the full eTool version:
5-68 HW eTool (Desmos)