The answer is correct, but the solution is convoluted. A straightforward algebraic solution is better. If the first digit is A and the rest of the number is B, then 10*B + A = 1.5*(A*10^k +B), for some positive integer k. Reworking the equation yields 17*B = A*(3*10^k-2). Since A is less than 10, it is relatively prime to 17. So, 17 must divide 3*10^k-2. Checking the residues for the integer values of k yields that the smallest k is 15. So A=1 and B = (3*10^15-2)/17.
Jun 17, 2014
by
Snow
