Money spending

Albert and Peter have an amount of money. If Albert spent $6 and Peter did not spend any, then the ratio of Albert's money to Peter's money is 1:3 . If Peter spent $6 and Albert did not spend any, the ratio of Albert's money to Peter's money is 3:7.How much money does each of them has?

Final Answer:

A =  36 USD
P =  90 USD

Step-by-step explanation:

$$\begin{gathered} (A-6):P=1:3 \\ A:(P-6)=3:7 \\ 3\cdot (A-6)=1\cdot P \\ 7\cdot A=3\cdot (P-6) \\ 3A-P=18 \\ 7A-3P=-18 \\ Pivot:Row1\leftrightarrow Row2 \\ Row2-\frac{3}{7}\cdot Row1\to Row2 \\ 0.29P=25.71 \\ P=\frac{25.71428571}{0.28571429}=90 \\ A=\frac{-18+3P}{7}=\frac{-18+3\cdot 90}{7}=36=36\text{USD} \\ A=36 \\ P=90 \end{gathered}$$

Try another example