If (X/4) = (Y/5) = (Z/9), then what is X : Y : Z?

Options

A. `8:10:19`
B. `4:5:9`
C. `45:36:20`
D. `15:12:7`

Answer

To solve the problem, we start with the equation given:

\[ \frac{X}{4} = \frac{Y}{5} = \frac{Z}{9} \]

Let's denote the common value of these fractions as \( k \). Therefore, we can express \( X \), \( Y \), and \( Z \) in terms of \( k \):

1. From \(\frac{X}{4} = k\):
\[ X = 4k \]

2. From \(\frac{Y}{5} = k\):
\[ Y = 5k \]

3. From \(\frac{Z}{9} = k\):
\[ Z = 9k \]

Now we have \( X \), \( Y \), and \( Z \) expressed in terms of \( k \):

- \( X = 4k \)
- \( Y = 5k \)
- \( Z = 9k \)

Next, we need to find the ratio \( X : Y : Z \):

\[ X : Y : Z = 4k : 5k : 9k \]

Since \( k \) is a common factor, we can cancel it out from the ratio:

\[ X : Y : Z = 4 : 5 : 9 \]

Thus, the final answer is:

\[ \text{The ratio } X : Y : Z = 4 : 5 : 9 \]