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.
2 Answers
justaguide | College Teacher | (Level 2) Distinguished Educator
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
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.