It is known that the arithmetic mean of two numbers is 12.65 and that one number is 1.6 more than the other.

It is known that the arithmetic mean of two numbers is 12.65 and that one number is 1.6 more than the other. Find these numbers.

Let the first number be equal to X. Then the second number is equal to (X + 1.6) (since it is 1.6 more than the first).
The arithmetic mean of numbers is their sum divided by the number of numbers themselves.
We have, by condition, two numbers, the arithmetic mean of which is 12.65.
Let’s compose and solve the resulting equation:
(X + (X + 1.6) / 2 = 12.65;
X + (X + 1.6) = 12.65 * 2;
X + X + 1.6 = 25.3;
2X = 25.3 – 1.6;
2X = 23.7;
X = 23.7: 2;
X = 11.85.
Thus, the first conceived number is 11.85.
Let’s find the second conceived number:
11.85 + 1.6 = 13.45 – the second planned number.
Let’s write down the answer.
Answer: 11.85; 13.45.