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

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