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Math Help - A bicycle question

  1. #1
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    Question A bicycle question

    Peter agreed to work after school for 8 weeks at a fixed weekly rate. But instead of being given only money, he was to be given $85 and a bicycle. However, Peter worked only 5 weeks at the fixed weekly rate and was given $25 and the bicycle. How much was the bicycle worth?

    -- I saw somewhere the answer is $75 but not sure how to get that.

    -- originally i took the $85 and divided by 8 weeks, and that gave me $10.62

    -- then i took the 5 weeks and multiplied it by $10.62

    -- that gave me 53.12

    -- thought about minusing $25 from that... but am totally STUMPED.

    p.s. yes, I know I am bad @ math!

    Thanks for reading!
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  2. #2
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    Quote Originally Posted by ronaldj View Post
    Peter agreed to work after school for 8 weeks at a fixed weekly rate. But instead of being given only money, he was to be given $85 and a bicycle. However, Peter worked only 5 weeks at the fixed weekly rate and was given $25 and the bicycle. How much was the bicycle worth?

    -- I saw somewhere the answer is $75 but not sure how to get that.

    -- originally i took the $85 and divided by 8 weeks, and that gave me $10.62

    -- then i took the 5 weeks and multiplied it by $10.62

    -- that gave me 53.12

    -- thought about minusing $25 from that... but am totally STUMPED.

    p.s. yes, I know I am bad @ math!

    Thanks for reading!
    Let w denote the money for work in 1 week and b the price of the bicycle.

    Then you know (talking about money only!):

    \left|\begin{array}{rcl}8w-b&=&85\\5w-b&=&25 \end{array} \right.

    Solve this system of equations for w and b
    Spoiler:
    I've got w = $20 and b = $75
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  3. #3
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    Many thanks Earboth!

    for your explanation and I LOVE the spoiler!! A nice way to do that part for the answer.

    No wonder you are a Super Member!

    Thanks again for your help.
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  4. #4
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    ...or use fact that you can use weekly rates:
    (b + 85) / 8 = (b + 25) / 5
    solve: b = 75
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