# A fitness instructor purchases excercise bikes and treadmills for two gyms.For the first Gym,2 excercise bike and 3 treadmills cost $2200.For the second Gym,3 excercise bike and 4 treadmills cost$3000.How much does a treadmill cost ?

Step-by-Step Solution:-

Let x and y be the price of exercise bike (e) and treadmill (t) respectively

The price of 2e and 3t is $2200: It means, 2x+3y=\$2200

Similarly,

The price of 3 exercises and 4 treadmill is $3000: It means, 3x+4y=\$3000

Find the x and y, using the equation:

2x+3y=\$2200\\ 3x+4y=\$3000


Now, using the Elimination Method:

Multiply, the first equation by 3 :

6x+9y=\$6600 Similarly, Multiply second equation by 2: 6x+8y=\$6000

Now, subtract first equation from second equation

6x+9y-(6x+8y)=\$6600-\$6000 \implies y=\$600 By solving we get, y=600 Now, Putting the Value of y in one of the equation 6x+9\times\$600=\$6600\implies 6x+\$5400=\$6600 \implies 6x=\$1200

Lets , say the first Equation, we get:

6x =\$1200\implies x =\$200

So,

Cost \ of \ a  \ treadmill = \\$600

Similar Post:

1. Solve |3h-3|<12. Then graph the solution set on a separate sheet of paper.