The arithmetic mean of the five numbers is (-3.2). If we add one more number x

The arithmetic mean of the five numbers is (-3.2). If we add one more number x to these numbers, then their arithmetic mean value will be: 2.4; Find x.

Let us denote by a1, a2, a3, a4 and a5 five numbers, the arithmetic mean of which is -3.2.

Then we can write the following relation:

(a1 + a2 + a3 + a4 + a5) / 5 = -3.2,

from which follows:

a1 + a2 + a3 + a4 + a5 = -3.2 * 5 = -16.

According to the condition of the problem, the arithmetic mean of these five numbers and the number x is 2.4, therefore, the following relationship takes place:

(a1 + a2 + a3 + a4 + a5 + x) / 6 = 2.4.

Using the ratio a1 + a2 + a3 + a4 + a5 = -16, we get:

(-16 + x) / 6 = 2.4.

We solve the resulting equation:

-16 + x = 6 * 2.4;

-16 + x = 14.4;

x = 16 + 14.4;

x = 30.4.

Answer: x = 30.4.