Find the digits a, b, and c of the two six digit numbers abcabc and ababab, given that
abcabc 55
------ = --
ababab 54
Please don't use a computer program for a PENCIL AND PAPER problem!
First simplify the left side
abcabc/ababab
= (1001*abc)/(10101*ab)
= (7*11*13*abc)/(3*7*13*37*ab)
= (11*abc)/(3*37*ab)
Then plug this into the given equation
(11*abc)/(3*37*ab) = 55/54
(11*abc)/(3*37*ab) = (5*11)/(3*18)
abc/(ab*37) = 5/18
abc/ab = 185/18
The digits a, b, and c are 1, 8, and 5 respectively.
Solution
