1. ## 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?

2. Originally Posted by Mr Rayon
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 $\displaystyle P$ be the money Maya would pay the plumber daily, and let $\displaystyle C$ represent the money Maya would pay the carpenter daily.

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

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

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

Therefore,

\displaystyle \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?

3. Originally Posted by Chris L T521
Does this make sense?
Yes. Thank you very much!