Modeling with Mathematics

Question

you have 40 minutes to exercise at the gym, and you want to burn 300 calories total using both machines. How much time should you spend on each machine?

Elliptical Trainer- 8 calories per minute

Stationary Bike- 6 calories per minute

Answer 1

It's a system of equations.

Let variable X = amount of time on elliptical trainor

Let Y = amount of time on bike

Equation 1 = Represents the amount of time on each equipment which = 40 minutes

X + Y = 40

Equation 2 = Represents the calories burnt on each equipment which = 300 minutes

8X + 6Y = 300

System:

X + Y = 40

8X + 6Y = 300

To Cancel out Y in System and solve for X, multiply the top equation by -6. Then plug back the value for X in either equation and solve for Y.

Ans: X=30

Y=10

Answer 2

E = time on elliptical

S = time on bike

E + S = 40

8E + 6S =300

Multiply equation 1 by 3 and divide equation 2 by 2

3E + 3S = 120

4E + 3S = 150

Subtract

E = 30

You take it from here!