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

Answer:

$x,y=7,8$

Step-by-step 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:

$\frac{4+6+x+y+10}{5}=\frac{20+x+y}{5}$

So we can say that:

$\frac{20+x+y}{5}=x$

Rearranging this, we get:

$\frac{20+x+y}{5}=x\\20+x+y=5x\\20+y=4x$

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.