13.354. When multiplying two numbers, one of which is 10 more than the other, a student made a mistake by reducing the tens digit of the product by 4. When dividing the obtained product by the smaller multiplier to check the answer, he got a quotient of 39 and a remainder of 22. Find the multipliers.
## Solution.

Let $x, y$ be the factors, $z$ be the erroneous product of numbers $x$ and $y$.

According to the condition, we have the system $\left\{\begin{array}{l}x-y=10, \\ x y=z+40, \\ z=39 y+22,\end{array}\right.$ from which $x=41, y=31$.

Answer: 31 and 41.