The arithmetic mean of the three numbers is 7, and the arithmetic mean of the other four is 12.5.

The arithmetic mean of the three numbers is 7, and the arithmetic mean of the other four is 12.5. what is the arithmetic mean of all seven numbers?

First of all, let’s calculate the sums of three numbers, if, according to the problem statement, their arithmetic mean is 7. To do this, we multiply the arithmetic mean by the number of numbers:

7 * 3 = 21.

The sum of these three numbers is 21.

Now let’s calculate the sum of four other numbers, the arithmetic mean of which is 12.5. Similarly, we find the sum of these four numbers:

12.5 * 4 = 50.

Let’s find the sum of all seven numbers by adding the sums found:

21 + 50 = 71.

To find the arithmetic mean of a new set of numbers consisting of 7 numbers, you need to divide their sum by the number of numbers, that is, by 7:

71: 7 = 10, 14 (approximately).