[ Decimal numeral system ]

Find a two-digit number that is 5 times the sum of its digits.

#
Note: The desired number must be divisible by 5.

## Solution

A number that is 5 times the sum of its digits must be divisible by 5. Therefore, it ends in 0 or 5. However, it cannot end in 0, because in that case it would be 10 times the sum of its digits. Thus, the desired number can be written in the form $10a + 5$. The sum of the digits of this number is $a + 5$. Therefore, we can set up the equation

$$
10a + 5 = 5(a + 5)
$$

Solving this, we get: $a = 4$, and the desired number is 45.

## Answer

45.