Double-digit 80970

Eva thought of two natural numbers. She first added these correctly, then subtracted them correctly. In both cases, she got a double-digit result. The product of the resulting two-digit numbers was 645. Which numbers did Eva think of? Please, what is this result?

Correct answer:

x =  29
y =  14

Step-by-step explanation:

$$\begin{gathered} (x+y)\cdot (x-y)=645 \\ 645=3\times 5\times 43=(3\cdot 5)\cdot 43=15\cdot 43 \\ x+y=43 \\ x-y=15 \\ x-(43-x)=15 \\ 2x=58 \\ x=\frac{58}{2}=29 \\ x=29 \end{gathered}$$

$$\begin{gathered} y=43-x=43-29=14 \\ \text{ Verifying Solution: } \\ a=x+y=29+14=43 \\ b=x-y=29-14=15 \\ s=a\cdot b=43\cdot 15=645 \end{gathered}$$

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