Money exchange

A told B, "If you give me 1/3 of your money, I'll have $50." In turn, B told A, "If you give me $9, we'll have the same amount." Find how much money each of them has.

Final Answer:

a =  42 USD
b =  24 USD

Step-by-step explanation:

$$\begin{gathered} a+b/3=50 \\ b+9=a-9 \\ 3a+b=150 \\ a-b=18 \\ Row2-\frac{1}{3}\cdot Row1\to Row2 \\ -1.33b=-32 \\ b=\frac{-32}{-1.33333333}=24 \\ a=\frac{150-b}{3}=\frac{150-24}{3}=42=42\text{USD} \\ a=42 \\ b=24 \end{gathered}$$

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