Problem Solving (PS) | Re: How many such positive integers exist so that if the unit digit of the

You should start by translating the problem to symbols:

old= 10r + u (i.e. r=1 u = 3 so 10*1 +3 = 13)
new=r

\(\frac{new}{old} = \frac{1}{14}\) so:

\(\frac{10r + u}{r} = \frac{1}{14}\)

which simplifies to:\(4r = u\)

now we can list posible solutionsstarting:

\(r=1 => u = 4\)
\(r=2 => u = 8\)
\(r=3 => u = 12\) wrong becauseu is unit number so must be smaller or equal to9

hence we have2 solutions