Question

Nando is on a rehabilitation program following a car accident. For the first month, he needs to exercise at most five hours per week and must burn at least 2,000 calories per week. The exercise he is allowed to

do is brisk walking which burns about 350 calories per hour and biking at a moderate pace which burns
about 700 calories per hour. Which graph best represents the set of all points that satisfy the system
representing Nando's exercise options?

Answer 1

See explanation

Explanation:

Let x be the number of hours per week Nando is brisk walking and y be the number of hours per week Nando is biking at a moderate pace.

For the first month, he needs to exercise at most five hours per week, then

`x+y\le 5`

Brisk walking burns about 350 calories per hour, then it burns 350x calories per x hours.

Biking at a moderate pace burns about 700 calories per hour, then it burns 700y calories per y hours.

Nando must burn at least 2,000 calories per week, so

`350x+700y\ge 2,000`

You get the system of two inequalities:

`\left\{\begin{array}{l}x+y\le 5\\ 350x+700y\ge 2,000\end{array}\right.`

The attached graph shows the solution set to this system of inequalities. In this diagram, red region represents the solution set to the first inequality, blue region represents the solution set to the second inequality and their intersection is the solution set to the system of two inequalities.