FORTNIGHT'S PUZZLE 9

PUZZLE 9: 8th-14th February (to be e-mailed by the 15th February)
POSTED BY IES CAMPANAR

DIGIT NUMBERS
Try to find all the two-digit numbers which, when divided by the sum of their digits, have a quotient equal to 7 with no remainder.

SOLUTION
The number in polynomial form is 10a+b. Because of the condition:(10a+b)/(a+b) = 710a+b = 7a + 7b3a = 6ba = 2bWith b= 1,2,3,4 (more it's impossible), the solutions are: 21, 42, 63, 84