IF 3a =2b and 4b=9c, find the ratio of a to c in simplest form and show steps.
from 3a + 2b , b = 3a/2
then in
4b = 9c
4(3a/2) = 9c
6a = 9c
a/c = 9/6 = 3/2
a:c = 3:2
or:
double the first: 6a = 4b
but 4b = 9c
so 6a = 9c
a/c = 9/6 = 3/2
Thanks.
To find the ratio of a to c in simplest form, we need to eliminate the variables b and solve for a and c individually.
Given:
3a = 2b ... (Equation 1)
4b = 9c ... (Equation 2)
From Equation 1, we can solve for b by isolating b:
b = (3a) / 2 ... (Equation 3)
Substituting Equation 3 into Equation 2, we can express c in terms of a:
4((3a)/2) = 9c
(6a) = 9c
c = (6a) / 9
c = (2a) / 3 ... (Equation 4)
Now, we have expressions for b and c in terms of a. So, let's determine the ratio of a to c by dividing the expression for a by the expression for c:
(a / c) = a / ((2a) / 3)
(a / c) = a * (3 / (2a))
(a / c) = (3 / 2)
Therefore, the ratio of a to c in simplest form is 3:2.