# Weight Loss and Gain

## Situation

Johnvir wants to gain muscle weight for an upcoming wrestling tournament while his sister, Chloe wants to lose weight since she is overweight and wants to be healthier. They both decide to go to the gym and these are their results:

## Johnvir Weight Gain

y=4x+105 or -4x+y-105=0

Variables:

• Y: Total Weight
• X: Number of Weeks
Johnvir weighs 105 pounds and starts to exercise and diet and gains 4 pounds a week.

## Chloe Weight Loss

y=-3x+210 or 3x+y-210=0

Variables:

• Y: Total Weight
• X: Number of Weeks
Chloe weighs 210 pounds and starts to exercise and diet and loses 3 pounds a weeks.

## Solution

y=4x+105 and y=-3x+210

We can isolate x

4x+105=-3x+210

4x+3x=210-105

7x=105

x=15

x=15 and so we sub in values for x and isolate y.

y=4*15+105

y=60+105

y=165

The coordinates of intersection are 15,165.

## Summary and Significance

Johnvir and Chloe will both be 165 pounds in 15 weeks. The significance of the solution is to show the week that both Chloe and Johnvir will have on the same week. Also, we use the graph to predict weights that they both will weigh and so they'll know when they can cut down on dieting or exercising.