given that 35 b equals 12 C find the ratio B:C in simplest form
To find the ratio B:C in simplest form, we can divide both sides of the equation 35B = 12C by the greatest common divisor (GCD) of 35 and 12.
The prime factorization of 35 is 5 * 7, and the prime factorization of 12 is 2^2 * 3.
The GCD of 35 and 12 is 1, since they do not share any common prime factors.
Dividing both sides by 1, we get:
(35B) / 1 = (12C) / 1
Simplifying, we arrive at:
35B = 12C
Now the ratio B:C is:
B/C = 12/35
Since there are no common factors between 12 and 35 (other than 1), the ratio B:C is already in simplest form.
Thus, the ratio B:C in simplest form is 12:35.