## 23. Division

Division of integers is performed. If the dividend is increased by 65 and the divisor is increased by 5, both the quotient and the remainder remain unchanged. What is this quotient?
23. Let $D$ - the dividend, $d$ - the divisor, $q$ - the quotient, and $r$ - the remainder. The conditions of the problem can be written as two equations:

$$
D=q d+r, \quad D+65=q(d+5)+r
$$

Subtracting the first equation from the second, we get

$$
65=5 q
$$

from which

$$
q=13
$$