Karan needs to choose between two gym plans. He can either pay a $ 1 5 0 $150dollar sign, 150 joining fee and a $ 1 0 $10dollar sign, 10 monthly fee, or he can pay a $ 5 0 $50dollar sign, 50 joining fee and a $ 3 0 $30dollar sign, 30 monthly fee. On what month will the cumulative costs of the plans be equal, and what will those total costs be? Karan will pay a cumulative cost of dollars with either plan to go to the gym for months.

Calculation for plan A:

Let numbe of months = x

Given that $10 is the monthly fee.

Given that $150 is the joining fee.

Then cost equation for plan A is given by:

A=10x+150

Calculation for plan B:

Let numbe of months = x

Given that $30 is the monthly fee.

Given that $50 is the joining fee.

Then cost equation for plan B is given by:

B=30x+50

Now we have to find on what month will the cumulative costs of the plans be equal.

So we will just set both equations equal to each other

10x+150=30x+50

150-50=30x-10x

100=20x

5=x

Hence it will take 5 months to make cost of both plans equal.

To find the total cost plug x=5 into any of above equations:

A=10x+150=10*5+150=50+150=200

Hence final cost will be $200.