Question

five whole numbers are written in order 4 6 x y 10 the mean and median are the same what are x and y values

Answer 1

`x,y=7,8`

Explanation:

4 6 x y 10

As x is the median number of this sequence, we know that the mean would be equal to this.

The mean is defined as:

`(4+6+x+y+10)/(5)=(20+x+y)/(5)`

So we can say that:

`(20+x+y)/(5)=x`

Rearranging this, we get:

`(20+x+y)/(5)=x\\20+x+y=5x\\20+y=4x`

As we know that:

`x, y \in \mathbb{R}\\y\geq x\\x,y \in \{6 \leq x,y \leq10 \}`

So we can substitute in values and see which fit the equality:

Subbing in x as 6 gives us,

`4(6)=20+y\\24=20+y\\y=4`

However, y must be bigger than x and must be between 6 and 10, so this is incorrect.

Subbing in x as 7 gives us,

`4(7)=20+y\\28=20+y\\8=y`

As 8 is bigger than 7, and is in between 6 and 10, this means all of our inequalities have been met and we have the correct answer.