The arithmetic mean of two numbers, one of which is 4 times less than the second is 10. Find these numbers.

Let x be the lesser of the numbers, then the second will be 4 times larger and denote it 4 * x.
The arithmetic mean of two numbers is the sum of these numbers divided by their number (by 2).
For our numbers, it will be like this: (x + 4x) / 2 = 10.
We solve the equation and find x.
5x / 2 = 10
5x = 20
x = 20: 5
x = 4 – the first number,
4 * x = 4 * 4 = 16 – the second number.
Let’s check (4 + 16) / 2 = 20/2 = 10.