Question

?A woman works out by running and swimming. When she runs, she burns 7 calories per minute. When she swims, she burns 8 calories per minute. She wants to burn at least 336 calories in her workout. Write an inequality that describes the situation.

Let x represent the number of minutes running and y the number of minutes swimming. Because x and y must be positive, limit the boarders to quadrant I only.

Answer 1

`7x+8y>=336`

Explanation:

Let

`x` be the number of minutes she runs, and

`y` be the number of minutes she swims.

Because she burns 7 calories/minute while running and 8 calories/minute while swimming the expression for the total number of calories she burns is

`7x+8y`

We want this quantity to be at least 336, so our inequality is

`7x+8y>=336`

Solving this for `y` we have

`y>=42-(7x)/8`

The advantage of putting the inequality in this form is that it makes it easier to plot. See the plot below.