Question

If the arithmetic mean of x,7,8 and 12 is 8, then find x?

Answer 1

`x=5`

Explanation:

If the arithmetic mean of the `color(green)4` numbers `x, 7, 8, and 12` is `color(blue)8`
then
`color(white)("XXX")(x+7+8+12)/color(green)4=color(blue)8`

`color(white)("XXX")rArr (x+27)/color(green)4=color(blue)8`

`color(white)("XXX")rArr (x+27)=color(green)4 * color(blue)8 = color(magenta)32`

`color(white)("XXX")rArrx=color(magenta)32-27=color(red)5`

Answer 2

`5`

Explanation:

the arithmetic mean is the sum of all the numbers in the set divided by how many numbers there are.

there are `4` numbers: `x, 7, 8` and `12`.

the arithmetic mean is the sum of all the numbers divided by `4`.

the arithmetic mean is `8`.

`8 * 4 = 32`

therefore the sum of all the numbers in the set is `32`.

`x + 7 + 8 + 12 = 32`

`x + 7 + 8 = 20`

`x + 7 = 12`

`x = 5`

an arithmetic mean of `8` gives the value of `x` as `5`.