# Math: Physical Fitness Facility?

A physical fitness facility is constructing an indoor running track with space for exercise equipment inside the track. The track must be at least 125 meters long, and the exercise space must have an area of at least 500 square meters.

a) Write and graph a system of inequalities that

describes the requirements of the facility.

(b) Find two solutions of the system and interpret their meanings in the context of the problem.

### 1 Answer

- jacob sLv 71 month agoFavorite Answer
a) Since the track must be 125 meters long, therefore.

2x + πy ≥ 125

Since the area of the exercise must be at least 500 sq meters , therefore .

xy ≥ 500

Also, x and y are positive. Therefore, the system of inequalities is

2x + πy ≥ 125

xy ≥ 500

x ≥ 0

y ≥ 0

Take the above 2x + πy ≥ 125 and xy ≥ 500 and graph it. I don't have a program to do graphs sorry.

let the y axis be 10 20 30 40 50 60 and the x axis be 10 20 30 40 50 60. plug it in your equations .