Question

If the mean of x + 2, 2x + 3, 3x + 4, 4x + 5 is x + 2, find x.

 

Answer 1

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