Question

22) Entre los ayudantes de cocina Juan y Rosa tienen $81.00. Si Juan pierde $36.00, el doble

de lo que le queda equivale al triple de lo que tiene Rosa ahora. ¿Cuánto tiene cada uno?.

Answer 1

Step-by-step explanation

Let's use J and R for the amount of money that Juan and Rosa have now, respectively. We are told that in total they have $81 which means that the sum of their money must be equal to 81:

`R+J=81`

Then we are told that "if Juan loses $36, twice that he has left is equal to three times what Rosa has now.

If Juan loses $36 then he will have J-36 dollars left. Twice this quantity is then:

`2\cdot(J-36)=2J-72`

And this must be equal to three times the amount of money that Rosa has now i.e. it must be equal to 3R. Then by equalizing these two expressions we obtain a new equation:

`2J-72=3R`

So we have two equations that we must use to find R and J:

`\begin{gathered} R+J=81 \\ 2J-72=3R \end{gathered}`

We can substract R from both sides of the first equation:

`\begin{gathered} R+J-R=81-R \\ J=81-R \end{gathered}`

Then we replace J with this expression in the second equation:

`\begin{gathered} 2J-72=3R \\ 2\cdot(81-R)-72=3R \\ 162-2R-72=3R \\ 90-2R=3R \end{gathered}`

Then we add 2R to both sides:

`\begin{gathered} 90-2R+2R=3R+2R \\ 90=5R \end{gathered}`

And we divide both sides by 5:

`\begin{gathered} (90)/(5)=(5R)/(5) \\ 18=R \end{gathered}`

Then we can find J:

`\begin{gathered} J=81-R=81-18 \\ J=63 \end{gathered}`Answer

Then the answer is:

Juan has $63 and Rosa has $18