five whole numbers are written in order (4, 6, x, y, 10). The mean and median of the five numbers are the same. Work out the values of x and y.

x = 7

y = 8

Step-by-step explanation:

Knowing that the mean is equal to the median, we can formulate the following equation:

⅕ (4 + 6 + x + y + 10) = x

Simplifying it, we get:

y = 4x - 20

Now, we know that both x and y are between 6 and 10 and that y is greater than x;

Mathematically, we have the conditions:

6 = < x = < 10

6 = < y = < 10

y > x

If we apply the second condition, i. e. the restrictions on the y-values, we find that x has to be between 6.5 and 7.5, i. e. 6.5 = < x = < 7.5;

This means x has to 7 since it can only be a whole number and this is the only whole number between 6.5 and 7.5;

Once we know this, we can find y simply by subbing it into the equation formulated previously:

y = 4 (7) - 20

y = 8