# 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.

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have a:b = 5:6 and b:c = 3: 7 We have to find (3c + 2a):a

Now a:b = 5:6 => a/b = 5/6

b:c = 3:7 => b/c = 3/7

(a/b)*(b/c) = (5/6)*(3/7)

=> a/c = 5/14

=> c/a = 14/5

(3c + 2a):a

=> 3c/a + 2a/a

=> 3(c/a) + 2

=> 3*14/5 + 2

=> 42/5 + 2

=> 52/5

The value of (3c+2a):a = 52/5

neela | High School Teacher | (Level 3) Valedictorian

Posted on

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.