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given that a+b/5 = b+c/6 = c+a/7 = k,

find the ratio a:b:c.

2 answers

I am sure you meant:
(a+b)/5 = (b+c)/6 = (c+a)7 = k

1st = 2nd: -----> 6a + 6b = 5b + 5c
b = 5c - 6a (#1)

1st and 3rd: ----> 7a+7b = 5a+5c
2a = 5c-7b (#2)

sub #1 into #2

2a = 5c - 7(5c-6a)
c = 4a/3

2nd and 3rd: 6a+6c = 7b+7c
c = 6a-7b (#3)

so 4a/3 = 6a - 7b
4a = 18a - 21b
21b = 14a
b = 2a/3

now..... finally

a : b : c = a : 2a/3 : 4a/3
= 1 : 2/3 : 4/3
= 3 : 2 : 4
thx...=]