\section*{Exercise 3 - V11033}

Fritz obtained the result of a division problem as 57 remainder 52. When he checked his work, he got 17380. This is incorrect because he had written the numbers unclearly and read a 6 as 0 in the tens place of the divisor during the check.

What is the correct problem? How did you find the result?
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The division problem given to Fritz is \(\frac{a}{b}\). Fritz calculates \(a=57 \cdot b+52\), performs the check, and gets \(57 \cdot b^{\prime}+52=17380\), where the factor \(b^{\prime}\) differs from the correct value \(b\) by the tens digit.

It follows that \(b^{\prime}=\frac{17380-52}{57}=304\). According to the problem statement, the actual value of \(b\) is obtained by replacing the tens digit 0 of \(b^{\prime}\) with 6. Therefore, \(b=364, a=57 \cdot 364+52=20800\), and the division problem given to Fritz is \(\frac{20800}{364}\).