We are given the following proportions:
[tex]\begin{gathered} x:y=3:9 \\ y:z=6:20 \end{gathered}[/tex]
The second proportion is equivalent to:
[tex]\frac{y}{z}=\frac{6}{20}[/tex]
Now, we substitute the value of "z":
[tex]\frac{y}{30}=\frac{6}{20}[/tex]
Now, we multiply both sides by 30:
[tex]y=30\times\frac{6}{20}[/tex]
Solving the operation we get:
[tex]y=9[/tex]
Now, since we have the value of "y" we can use the first proportion to get the value of "x":
[tex]x_:y=3:9[/tex]
This is equivalent to:
[tex]\frac{x}{y}=\frac{3}{9}[/tex]
Now, we substitute the value of "y":
[tex]\frac{x}{9}=\frac{3}{9}[/tex]
Now, we multiply both sides by 9:
[tex]x=9\times\frac{3}{9}[/tex]
Solving the operations:
[tex]x=3[/tex]
Therefore, the value of "x" is 3.
