Question

Given a set `{12, x ,17}`, for what x would the mean be 14?

Answer 1

`x=13`

Explanation:

`color(white)(xx)bar a =1/nsum_(i=1)^n a_i` (the mean of a set of n data points)

`color(white)(xx)14=1/3sum_(i=1)^3 a_i`
`=>(12+x+17)/3=14`

Multiply both sides by `3`
`color(white)(xx)color(red)(3*)(12+x+17)/3=color(red)(3*)14`
`=>x+29=42`

Add `-29` to both sides
`color(white)(xx)x+29color(red)(-29)=42color(red)(-29)`
`=>x=13`