please help

Question

ginny is playing a video game where her character can have a maximum of 100 health points. She wants to look for gold pieces in a swamp, but while swimming in the swamp, her character will lose 3.5 health points per second. She wants to enter the swamp with a full 100 health points, and exit the swamp with at least 25 health points remaining. Write an inequality to represent the situation, and use it to find how many seconds ginnys character can spend in the swamp.

Answer 1

P(t) = number of health points as a function of time in the swamp; t in seconds

 

P(t) = 100 - 3.5t

 

To exit with at least 25 health points,

 

100 - 3.5t ≥ 25

 

To find maximum allowable time in swamp, solve for t from

 

100 - 3.5t = 25 

 

t = (100 - 25)/3.5 s = 75/3.5 s ≅ 21.43 s

 

It is more conservative to round down, so she must not spend more than 21.4 s in the swamp.

Answer 2

The inequality will be 100-(3.5)≥25, where s is the time in seconds. So,

 

75≥(3.5)s

s≤75/3.5

 

75/3.5 is approximately 21.43, so ginny can be at most 21 seconds in the swap.