Monthly income

There are three working people - X, Y, Z. The average monthly income of X and Y is 5050 USD.The average monthly income of Y and Z is 6250 USD, and the average monthly income of X and Z is 5200 USD. What is monthly income of X?

Final Answer:

X =  4000 USD

Step-by-step explanation:

$$\begin{gathered} \frac{X+Y}{2}=5050 \\ \frac{Y+Z}{2}=6250 \\ \frac{X+Z}{2}=5200 \\ X+Y=5050\cdot 2 \\ Y+Z=6250\cdot 2 \\ X+Z=5200\cdot 2 \\ X+Y=10100 \\ Y+Z=12500 \\ X+Z=10400 \\ Row3-Row1\to Row3 \\ -Y+Z=300 \\ Row3+Row2\to Row3 \\ 2Z=12800 \\ Z=\frac{12800}{2}=6400 \\ Y=12500-Z=12500-6400=6100 \\ X=10100-Y=10100-6100=4000=4000\text{USD} \\ X=4000 \\ Y=6100 \\ Z=6400 \end{gathered}$$

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