# Question fc7ce

May 22, 2017

See a solution process below:

#### Explanation:

The formula for calculating the percent change in a value between two points in time is:

$p = \frac{N - O}{O} \cdot 100$

Where:

$p$ is the percent change - what we are solving for in this problem.

$N$ is the New Value - 7 pounds in this problem.

$O$ is the Old Value - 12 pounds in this problem.

Substituting and solving for $p$ gives:

$p = \frac{7 - 12}{12} \cdot 100$

$p = - \frac{5}{12} \cdot 100$

$p = - \frac{500}{12}$

$p = 41.7$ rounded to the nearest tenth.

Phil's weight changed color(red)(-41.7%) during hibernation.

To gain his weight back Phil would go from $7$ pounds (this is now the Old Value) to $12$ pounds (this is now the New Value).

Substituting these values into the formula gives:

$p = \frac{12 - 7}{7} \cdot 100$

$p = \frac{5}{7} \cdot 100$

$p = \frac{500}{7}$

$p = 71.4$ rounded to the nearest tenth.

Phil would need to add color(red)(71.4%)# of his weight to get to the weight he was before hibernating.