What two digit number is twice the product of its digits
Is there a way to solve this problem purely algebraically? I was able to solve it by inspection (I got 36). I have been working at it for an hour or so, any ideas? As in, solving as a system of equations
It should be the solution to $ 10a+b = 2ab $
Best Answer
If the 2 digit num is $ab$ then $10a+b=2ab$ and so $(2a-1)(b-5)=5$. This forces $b-5=1$ (since $b-5<5$) and $2a-1=5$ so that $ab=36$.