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Let's suppose that

$$10,a+15,ba +15,3 = 2\times (20, ab)$$

where numbers are in their decimal representation, and so $ab$ and $ba$ are two digit numbers. Is there a straightforward way to evaluate $a\times b$? One approach is to write down

$$10+\frac{a}{10}+15+\frac{10b+a}{100}+15+\frac{3}{10} = 2\times (20+\frac{10a+b}{100})$$

Prime Mover
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1 Answers1

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You are on the right track. The next step is to simplify the expression. The expression simplifies to

$$\frac{3}{10} - \frac{9}{100} a + \frac{8}{100} b = 0$$

and this simplifies further once you multiply it by $100$ to

$$9a-8b=30$$

5xum
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