Question

Find the ratio a : b, given each equality.
5a + 3b =6b

Answer 1

To find the ratio \( a : b \) given the equation \( 5a + 3b = 6b \), we can start by simplifying the equation.

1. Rearrange the equation to isolate terms involving \( a \) and \( b \):
\[
5a + 3b - 6b = 0
\]
This simplifies to:
\[
5a - 3b = 0
\]

2. Now, we can solve for \( a \) in terms of \( b \):
\[
5a = 3b
\]
\[
a = \frac{3b}{5}
\]

3. To find the ratio \( a : b \), we express \( a \) in terms of \( b \):
\[
\frac{a}{b} = \frac{3b/5}{b} = \frac{3}{5}
\]

This means that the ratio \( a : b \) can be written as:
\[
a : b = 3 : 5
\]

Thus, the ratio \( a : b \) is \( \boxed{3 : 5} \).