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Math Help - money

  1. #1
    Member Mr Rayon's Avatar
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    money

    Maya needs to renovate her house. She has enough money to pay a plumber for 28 days or a carpenter for 21 days. For how many days can she pay the tradesmen if they both work at the same time? If Maya's next pay cheque will come in 2 weeks, can she afford to hire both specialists till then?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Mr Rayon View Post
    Maya needs to renovate her house. She has enough money to pay a plumber for 28 days or a carpenter for 21 days. For how many days can she pay the tradesmen if they both work at the same time? If Maya's next pay cheque will come in 2 weeks, can she afford to hire both specialists till then?
    Let P be the money Maya would pay the plumber daily, and let C represent the money Maya would pay the carpenter daily.

    Then if the total amount of money Maya has is T_0 dollars, it follows that the daily pay for the plumber is 28P=T_0\implies P=\tfrac{1}{28}T_0 and the daily pay for the carpenter is 21C=T_0\implies C=\tfrac{1}{21}T_0

    Now, let us say D_0 is the number of days she pays both of them to work.

    So we want to solve D_0\left(P+C\right)=T_0\implies D_0\left(\tfrac{1}{28}T_0+\tfrac{1}{21}T_0\right)=  T_0 for D_0

    Therefore,

    \begin{aligned}D_0\left(\tfrac{1}{28}T_0+\tfrac{1}  {21}T_0\right)=T_0 & \implies D_0\left(\tfrac{1}{28}+\tfrac{1}{21}\right)=1\\ & \implies D_0\left(\tfrac{3}{84}+\tfrac{4}{84}\right)=1\\ & \implies D_0\left(\tfrac{7}{84}\right)=1\\ & \implies\tfrac{1}{12}D_0=1\\& \implies D_0=12\end{aligned}

    Therefore, Maya has enough money to pay both the plumber and the carpenter for 12 days. Given this, she won't have enough money to last her until her paycheck.

    Does this make sense?
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  3. #3
    Member Mr Rayon's Avatar
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    Quote Originally Posted by Chris L T521 View Post
    Does this make sense?
    Yes. Thank you very much!
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