The vet told jake that his dog, rocco, who weighed 55 pounds, needed to lose 10 pounds. jake started walking rocco every day and changed the amount of food he was feeding him. rocco lost half a pound the first week. jake wants to determine rocco’s weight in pounds, p, after w weeks if rocco continues to lose weight based on his vet’s advice.
the equation of the scenario is .
the values of p must be .

Hey there!

If Rocco loses a half of a pound, or 0.5 pounds, per week, we could multiply that number by the amount of weeks it's been since Jake first started counting in order to find the total weight that Rocco's lost. That would be represented by 0.5w, where, as your question states, w is the number of weeks. You would subtract this from Rocco's initial weight, which is 50, and you would find p after plugging in the number of weeks. 

So, all together, that looks like:

p = 50 – 0.5w

That's the answer to your first part. The second part just requires you to plug in a couple numbers for w. For example:

p = 50 – 0.5w
p = 50 – 0.5(1)
p = 50 – 0.5
p = 49.5

p = 50 – 0.5w
p = 50 – 0.5(2)
p = 50 – 1
p = 49

Just solve as many numbers as your problems tells you to like this. If you wanted to find how many weeks it would take Rocco to hit 40 pounds, you could plug in 40 for p and solve for w. 

   40 = 50 – 0.5w
– 50 – 50

–10 = –0.5w
–0.5    –0.5

20 = w

So, it would take Rocco 20 weeks to get to 40 pounds. 

Hope this helped you out! :-)