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?

Correct answer:

X =  4000 USD

Step-by-step explanation:

X+Y2=5050 Y+Z2 = 6250 X+Z2 = 5200  X+Y=5050⋅ 2 Y+Z=6250⋅ 2 X+Z=5200⋅ 2  X+Y=10100 Y+Z=12500 X+Z=10400  Row3−Row1→Row3 X+Y=10100 Y+Z=12500 −Y+Z=300  Row3+Row2→Row3 X+Y=10100 Y+Z=12500 2Z=12800  Z=128002=6400 Y=12500−Z=12500−6400=6100 X=10100−Y=10100−6100=4000=4000 USD  X=4000 Y=6100 Z=6400\dfrac{ X+Y }{ 2 } = 5050 \ \\ \dfrac{ Y+Z }{ 2 } \ = \ 6250 \ \\ \dfrac{ 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 \ \\ \ \\ Row 3 - Row 1 → Row 3 \ \\ X+Y = 10100 \ \\ Y+Z = 12500 \ \\ -Y+Z = 300 \ \\ \ \\ Row 3 + Row 2 → Row 3 \ \\ X+Y = 10100 \ \\ Y+Z = 12500 \ \\ 2Z = 12800 \ \\ \ \\ Z = \dfrac{ 12800 }{ 2 } = 6400 \ \\ Y = 12500-Z = 12500-6400 = 6100 \ \\ X = 10100-Y = 10100-6100 = 4000 = 4000 \ \text{USD} \ \\ \ \\ X = 4000 \ \\ Y = 6100 \ \\ Z = 6400

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statisticsalgebrabasic operations and conceptsUnits of physical quantitiesGrade of the word problem

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