Question

Karan needs to choose between two gym plans. he can either pay a $150 joining fee and a $10 monthly fee, or he can pay a $50 joining fee and a $300 monthly fee
On what month will the cumulative costs of the plans be equal, and what will those total cost be?

Answer 1

Solution:

Let the cumulative costs of the plans will be equal after x months.

Then we can write

$150+10x=50+300x\\ \\ 150-50=300x-10x\\ \\ 100=290x\\ \\ x=\frac{100}{290}\\ \\ x=\frac{10}{29}$

Hence after 10/29th Month cost will be equal.

and that cost$=150+\frac{10}{29} *10=\frac{4450}{29}$ $