Two-digit 82521

Karel had to multiply two two-digit numbers. Out of care, he changed the order of the digits in one of the factors and got a product that was 4,248 less than the correct result. What is the correct result?

How much should Karl have earned?

Correct answer:

x₁ =  5369
x₂ =  4720

Step-by-step explanation:

$$\begin{gathered} 4248=2\times 2\times 2\times 3\times 3\times 59=2^3\times 3^2\times 59 \\ x=ab\cdot cd=ab\cdot dc+4248 \\ 59\cdot 91=59\cdot 19+4248 \\ 59\cdot 91=59\cdot 19+59\cdot 72 \\ 91=19+72 \\ {x}_1=59\cdot 91=5369 \end{gathered}$$

$$\begin{gathered} x_2=ab\cdot cd=ab\cdot dc+59\cdot 72 \\ 59\cdot 80=59\cdot 08+59\cdot 72 \\ 59(80-8)=59\cdot 72 \\ 59\cdot 72=59\cdot 72 \\ {x}_2=80\cdot 59=4720 \end{gathered}$$

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