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Question
If the mean of x + 2, 2x + 3, 3x + 4, 4x + 5 is x + 2, find x.
Solution
The given data is x+2, 2x+3, 3x+4, 4x+5. They are four in numbers.
The mean is
`((x+2)+(2x+3)+(3x+4)+(4x+5))/4`
`=(x+2+2x+3+3x+4+4x+5)/4`
`=(10x+14)/4`
`=(2(5x+7))/4`
`=(54x+7)/2`
But, it is given that the mean is x+2. Hence, we have
`(5x+7)/2=x+2`
⇒ 5x +7 =2(x+2)
⇒5x +7 = 2x + 4
⇒ 5x -2x = 4-7
⇒ 3x = -3
`⇒x =-3/3`
⇒ x =-1
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