Question

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
.

Answer 1

To determine Rocco’s weight \( p \) after \( w \) weeks, we can establish an equation based on the information provided.

Rocco's starting weight is 55 pounds, and he needs to lose 10 pounds. The weight loss can be expressed in the equation:

\[
p = 55 - (0.5w)
\]

where:
- \( p \) is Rocco's weight in pounds after \( w \) weeks,
- 0.5 represents the weight loss of half a pound per week,
- \( w \) is the number of weeks.

Now, as for the values of \( p \), Rocco's weight must be non-negative and should not go below 45 pounds since he needs to lose 10 pounds from his starting weight of 55 pounds.

Thus, the values of \( p \) must be:

\[
p \geq 45
\]

This means that as long as \( w \) is less than or equal to 20 (because \( 55 - 0.5(20) = 45 \)), we maintain valid values for \( p \).

In summary:
- The equation is \( p = 55 - 0.5w \).
- The values of \( p \) must be \( p \geq 45 \).