# Thread: Linear Word Problem help

1. ## Linear Word Problem help

Rachael and Sabine belong to different local gyms. Rachael pays $35 per month and a one-time registration fee of$15. Sabine pays only $25 per month but had to pay a$75 registration fee. After how many months will Rachael and Sabine have spent the same amount on their gym memberships?

2. Originally Posted by sri340
Rachael and Sabine belong to different local gyms. Rachael pays $35 per month and a one-time registration fee of$15. Sabine pays only $25 per month but had to pay a$75 registration fee. After how many months will Rachael and Sabine have spent the same amount on their gym memberships?
Let x be month
Rachael = $35 per month,$15
Sabine = $25 per month,$75

35x + 15 = 25x + 75
10x = 60
x = 6 months

3. Originally Posted by sri340
Rachael and Sabine belong to different local gyms. Rachael pays $35 per month and a one-time registration fee of$15. Sabine pays only $25 per month but had to pay a$75 registration fee. After how many months will Rachael and Sabine have spent the same amount on their gym memberships?
To start, let's declare some variables.

Let x be the number of months paid for,
and let y be the the total amount paid for gym memberships.

Rachael Pays 15 dollars to start, and 35 dollars per month. So lets start off that equation as $\displaystyle y=15+35x$ Remember that y = the total amount paid for the membership, which for any given month, will be 15 plus 35 for each month previous.

Sabines equation follows from the same rationale to be $\displaystyle y=75+25x$.

Now what do we know about how to find where 2 linear equations have a same variable. (Keep in mind the question is asking for the number of months until both have paid the same amount) So if we set both equation's y value equal, we know that if we solve for x, we are finding the x value that is valid for both equations giving the same total amount paid for the gym, and therefore finding the number of months.

$\displaystyle y=15+35x \ \ \ \ y=75+25x$

$\displaystyle 75+25x=15+35x$

$\displaystyle 60 = 10x$

$\displaystyle x= 6$

Therefore Rachael and Sabine have paid the same amount after x=6 months. Does this help?

4. That's a better solution Kasper. I'll learn from that.