Question

You have 40 minutes to exercise at the gym. Elliptical Trainer burns 8.2 calories per minute and stationary bikes burn 6.5 calories per minute. You want to burn 294 calories total using both machines. How much time should you spend on each machine? You may use either the substitution or elimination method, but show all work for full credit.

Answer 1

To burn 294 calories in 40 minutes, you should spend 20 minutes on the elliptical trainer and 20 minutes on the stationary bike.

Step-by-step explanation:

To determine how much time should be spent on each machine to burn 294 calories in 40 minutes, we can use a system of equations and the substitution method.

Let x be the number of minutes spent on the elliptical trainer, and y be the number of minutes spent on the stationary bike. Then, the two equations based on the given information are:

1. 8.2x + 6.5y = 294 (calories equation)
2. x + y = 40 (time equation)

Using the substitution method, solve the second equation for y: y = 40 - x.

Substitute y in the calories equation with the expression found:

8.2x + 6.5(40 - x) = 294

Simplify the equation:

8.2x + 260 - 6.5x = 294

1.7x = 34

Divide both sides by 1.7 to find x:

x ≈ 20 minutes

Now, substitute x back into the time equation to find y:

y = 40 - 20 = 20 minutes

You should spend 20 minutes on the elliptical trainer and 20 minutes on the stationary bike to burn a total of 294 calories.