If a:b= 5:6 and b:c= 3:7, what is the value of (3c+2a):a? Express your answer as a common fraction.

Given a:b = 5: 6 and b:c =
3:7.

We have to find the value of
(3c+2a):a.

Solution:

We
rewrite fractions as below:

a/b = 5/6. So a =
5b/6

b/c = 3/7. So  b = =
3c/7.

Therefore  a = 5b/6 = (5/6)(3c/7) =
5c/7.

Thus we expressed a = 5c/7 and  b = 3c/7 in terms of
c.

Thererore (3c+2a):a = {3c+2*5c/7}:(5c/7) . We multiply
both terms on the right side by 7.

=> (3c+2a):a =
7(3c+2*5c/7): (5c)

=> (3c+2a):a = (21c+10c):
5c

=> (3c+2a):a = (31c):5c. We divide the terms on
the right by c.

=> (3c+2a):a = 31:5. Or (3x+2a)/a =
31/5 .

So (3c+2a)/a =
31/5.