# ?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.

May 2, 2018

$7 x + 8 y \ge 336$

#### 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

$7 x + 8 y$

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

$7 x + 8 y \ge 336$

Solving this for $y$ we have

$y \ge 42 - \frac{7 x}{8}$

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