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Math Help - Linear Word Problem help

  1. #1
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    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?
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  2. #2
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    Quote Originally Posted by sri340 View Post
    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
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  3. #3
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    Quote Originally Posted by sri340 View Post
    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 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 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.

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

    75+25x=15+35x

    <br />
60 = 10x

    <br />
x= 6

    Therefore Rachael and Sabine have paid the same amount after x=6 months. Does this help?
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  4. #4
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    That's a better solution Kasper. I'll learn from that.
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