Find the digits a, b, and c of the two six digit numbers abcabc and ababab, given that
abcabc 55
------ = --
ababab 54
Solution:
185185 55
--------- = --- = 1.0185185 ...
181818 54
Analytic solution:
54*1001*abc = 55*10101*ab
5405400a + 540540b + 54054c = 5555550a + 555555b
54054c = 150150a + 15015b
gcd is 3003
18c = 50a + 5b
clearly 18c is a multiple of 5
so c=5
90 = 50a + 5b
18 = 10a + b clearly a=1 and b=8
(a,b,c) = (1,8,5)
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Posted by Larry
on 2025-01-20 12:26:16 |
Analytic solution
