13.184. If the student had correctly multiplied two numbers written on the board, the product would have been 4500. However, while copying the factors from the board, the student wrote a 3 instead of the last digit 5 in one of them and obtained 4380 after multiplication. What numbers should the student have multiplied?
Solution.

Let $10 x+5$ be the first number, $y$ be the second. Then $\left\{\begin{array}{l}(10 x+5) y=4500, \\ (10 x+3) y=4380,\end{array}\right.$ from which $x=7$, the first number $10 \cdot 7+5=75 ; y=60$.

Answer: 75 and 60.