#7: At the gym on Saturday, Reese ran 5 miles on the treadmill and then
completed 1 mile on the elliptical machine, and burned 725 calories. On Sunday
she ran 3 miles on the treadmill and completed 1 mile on the elliptical, and burned
505 calories. Write and solve a linear system to find the number of calories Reese
burns on each machine.
Treadmill:
Elliptical:

The equations are 5t + e = 725 and 3t + e = 505

Step-by-step explanation: We shall start by assigning letters to the unknown variables, hence we shall call the treadmill t, and we shall call the elliptical machine e.

If on Saturday, she ran 5 miles on the treadmill and 1 mile on the elliptical machine and she burned 725 calories in the process, we can express this as

5t + e = 725 (1)

Also on Sunday, she ran 3 miles on the treadmill and 1 mile on the elliptical machine and burned 505 calories in the process, that too can be expressed as

3t + e = 505 (2)

We now have a pair of simultaneous equations which an be solved by the elimination method (reason being that on of the unknowns have the same coefficient, that is variable e).

Subtract equation (2) from equation (1) and you arrive at;

2t = 220

Divide both sides of the equation by 2

t = 110

Having calculated the value of t, substitute for the value of t into equation (1)

5t + e = 725

5(110) + e = 725

550 + e = 725

Subtract 550 from both sides of the equation

e = 175

The above calculations shows that the calories burned on each gym equipment are;

Treadmill = 110 per hour

Elliptical = 175 per hour