7.1. In a four-digit number, Petya erased the first digit and obtained a three-digit number. Then he divided the original number by this three-digit number and got a quotient of 3, with a remainder of 8. What is the original number? (Find all possible numbers).
Answer: 1496 or 2996. Solution. Let $x$ be the first digit, $y$ be the three-digit number obtained after crossing out the first digit. Then $1000 x+y=3 y+8$, i.e., $500 x=y+4$. From this, considering the inequalities $0<y<1000$, we get that $x$ is either 1 or 2. Then, respectively, $y=496$ or $y=996$.