High School

Choose the best answer. If necessary, use the paper you were given.

If [tex]\frac{3b}{2c} = \frac{9}{5}[/tex], what is the value of [tex]\frac{9b}{6c}[/tex]?

A. [tex]\frac{3}{2}[/tex]
B. 466
C. 46
D. [tex]\frac{9}{5}[/tex]
E. [tex]\frac{9}{2}[/tex]
F. [tex]\frac{27}{5}[/tex]

Answer :

We start with the given equation:

[tex]$$
\frac{3b}{2c} = \frac{9}{5}.
$$[/tex]

Notice that the left-hand side can be written as:

[tex]$$
\frac{3b}{2c} = \frac{3}{2} \cdot \frac{b}{c}.
$$[/tex]

This means that:

[tex]$$
\frac{3}{2} \cdot \frac{b}{c} = \frac{9}{5}.
$$[/tex]

To find [tex]$\frac{b}{c}$[/tex], multiply both sides by [tex]$\frac{2}{3}$[/tex]:

[tex]$$
\frac{b}{c} = \frac{9}{5} \cdot \frac{2}{3} = \frac{18}{15} = \frac{6}{5}.
$$[/tex]

Next, we want to find the value of:

[tex]$$
\frac{9b}{6c}.
$$[/tex]

We can simplify this expression:

[tex]$$
\frac{9b}{6c} = \frac{9}{6} \cdot \frac{b}{c} = \frac{3}{2} \cdot \frac{b}{c}.
$$[/tex]

Now substitute the value we found for [tex]$\frac{b}{c}$[/tex]:

[tex]$$
\frac{3}{2} \cdot \frac{6}{5} = \frac{18}{10} = \frac{9}{5}.
$$[/tex]

Thus, the final answer is:

[tex]$$
\frac{9}{5}.
$$[/tex]