3. The mentor gave the student to divide one number by another. The student got a quotient of 74 and a remainder of 22. Then he performed a check: he multiplied the quotient by the divisor and added the remainder to the product, thus obtaining 30214. It turned out that there was an error.

The student, while multiplying (during the check), read a six in the tens place of the divisor as a zero. Determine the dividend and the divisor.
Solution. Let's denote the dividend by $x$, and the divisor by $y$. According to this, $x=74 y+22$. During the verification, i.e., when calculating $74 y+22$, the student made a mistake, and the obtained number is not correct, which means it needs to be corrected. How? In the multiplication $74 y$, the student, taking zero instead of six in the tens place, effectively did not multiply by 6 tens, so his trial result is smaller by $74 \cdot 60=4440$. Therefore, the result needs to be increased by 4440, so we have

$$
74 y+22=30214+4440 \text{, i.e., } y=468
$$

Finally, the divisor is 468, and the dividend is 34654.