If 3A = 5 B and 4B = 6C then find A:C?

Answer 1

To find the ratio of A to C, we can first find the values of A, B, and C using the given equations.

From the first equation:
3A = 5B
A = 5B/3

From the second equation:
4B = 6C
B = 6C/4
B = 3C/2

Substitute the value of B in terms of C from the first equation into the second equation:
5(3C/2)/3 = 3C/2
15C/6 = 7C/2
15C = 21C
C = 15/21
C = 5/7

Now substitute the value of C back into the equation for B:
B = 3(5/7)/2
B = 15/14

And finally, substitute the value of B back into the equation for A:
A = 5(15/14)/3
A = 25/14

Therefore, the ratio of A to C is:
A:C = (25/14) : (5/7)
A:C = 25*7 : 14*5
A:C = 175 : 70
A:C = 25 : 10
A:C = 5 : 2

So, the ratio of A to C is 5:2.