Mike weigha 200 pounds and pland to lose 1.5 pounds a week. jeff weighs 180 pounds ans plans to lose 0.5 pound a week. when will mike and jeff weigh the same

Set up two linear equations for each of them:
For Mike
Initial weigh 200 pounds
Rate of loss: 1.5 pound / week
Variables:
(x) = number of weeks
y = weigh at (x) number of weeks

Let's set the equation:
-1.5 pounds per week (times) number of week = -1.5 (x) (This will give the weight of Mike after x number of weeks
Since Mike starts of at 200 pounds
y = -1.5(x) + 200

Note: The Rate is negative (-1.5x) because it is decreasing.

For Jeff do the same
Rate of loss= 0.5 pounds/week
Initial Weight = 180 pounds

Equation: y= -0.5(x) + 180

TO FIND OUT WHEN THEY WILL WEIGHT THE SAME
Just make them equal to each other

y=-1.5(x) + 200
y= -0.5(x) +180

-1.5(x) +200 = -0.5(x) + 180

Move (x) variables to one side

-1.5(x) + 0.5(x) = 180 - 200

-1(x) = -20

Minus cancels out

(x)= 20

So Mike and Jeff will weigh the same after 20 weeks