Question

At New years you decide to join a gym to lose all those calories gained during winter break and youre comparing two different gyms. The first gym, gym A has a 12$ initiation fee and then costs 10$ per month. The second gym , gym B has a 20$ initiation fee and then costs 6$ per month. Create an equation that aims to find when these two gyms will cost the same amount of money

Answer 1

Given:

For gym A, initiation fee = $12 and cost = $10 per month.

For gym B, initiation fee = $20 and cost = $6 per month.

To find:

The equation that aims to find when these two gyms will cost the same amount of money,

Solution:

Let the number of months be x.

Cost function = Initiation fee + (cost)(x)

Cost function for gym A is

$f(x)=12+10x$

Cost function for gym B is

$g(x)=20+6x$

Cost of these two gyms are equal if f(x)=g(x).

$12+10x=20+6x$

Therefore, the required equation is $12+10x=20+6x$.

On solving this equation, we get

$10x-6x=20-12$

$4x=8$

$x=2$

Hence, after 2 months the cost of these two gyms are same.