Answer: choice B) 9/70
===========================================================
Explanation:
Start with the second equation and isolate 4b by multiplying both sides by 3c
(4b)/(3c) = 1/7
4b = 3c/7
Now multiply both sides by 1/2 to get
4b*(1/2) = (3c/7)*(1/2)
2b = 3c/14
That will be plugged into the '2b' of the first equation
a/(2b) = 3/5
a/(3c/14) = 3/5
(a/1) divided by (3c/14) = 3/5
(a/1)*(14/(3c)) = 3/5
(a*14)/(1*3c) = 3/5
(14a)/(3c) = 3/5
(a/c)*(14/3) = 3/5
The last step is to multiply both sides by 3/14 to isolate a/c
(a/c)*(14/3) = 3/5
(a/c)*(14/3)*(3/14) = (3/5)*(3/14)
a/c = (3*3)/(5*14)
a/c = 9/70
So that's why the answer is choice B) 9/70
------------------
An alternative way to get the answer is to first isolate 'a' in the first equation
Use cross multiplication
a/(2b) = 3/5
5a = 6b
a = 6b/5 <-- call this equation (3)
Do the same for 'c' in the second equation
(4b)/(3c) = 1/7
7*4b = 3c*1
28b = 3c
3c = 28b
c = 28b/3 <-- call this equation (4)
Divide equation (3) over equation (4)
a/c = (6b/5) divided by (28b/3)
a/c = (6b/5)*(3/(28b))
a/c = (6b*3)/(5*28b)
a/c = 18/140
a/c = (9*2)/(70*2)
a/c = 9/70
------------------
Either way, the answer is 9/70
