High School Algebra

Question

You want to burn 400 calories exercising at the gym. The elliptical trainer burns 10 calories per minute, while the treadmill burns 8 calories per minute. Determine the intercepts for each of the machines.

SOMEONE HELP I DONT KNOW HOW TO SOLVE IT

Answer 1

Elliptical: (0, 400), (40, 0)

Treadmill: (0, 400), (50, 0)

Answer 2

Basically the intercept means one is zero. x-intercept means y is zero (where does the function cross the x axis when y is zero). y-intercept means x is zero.

Let E = time on the elliptical machine and T = time on the Treadmill. So we get

(10 calories per minute) * (minutes on Elliptical) + (8 calories per minute) * (minutes on Treadmill) = 400 calories)

[note: notice how the units cancel out just as if they were a variable: (calories/minute)•(minutes) = calories]

So our formula is:

10E + 8T = 400

Solving for the variable E, we have

10E = 400 - 8T ⇒ E = 40 - 0.8T

If T = 0 (intercept), then E = 40. Similarly, if E = 0, then 0.8T = 40 or T = 50. So your intercepts for the machines are 40 for Elliptical, 50 for Treadmill.