Answer:
The correct option is 4.
Step-by-step explanation:
It given that recipe ingredients remain in a constant ratio no matter how many servings are prepared.
It means the relation between x and y is
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
where k is constant of proportionality.
We need to find a possible ratio table for ingredients X and Y for the given number of servings.
In table 1,
[tex]\frac{y_1}{x_1}=\frac{2}{1}[/tex]
[tex]\frac{y_2}{x_2}=\frac{3}{2}[/tex]
[tex]\frac{y_1}{x_1}\neq \frac{y_2}{x_2}[/tex]
Option 1 is incorrect.
In table 2,
[tex]\frac{y_1}{x_1}=\frac{2}{1}=2[/tex]
[tex]\frac{y_2}{x_2}=\frac{4}{2}=2[/tex]
[tex]\frac{y_3}{x_3}=\frac{8}{3}[/tex]
[tex]\frac{y_1}{x_1}\neq \frac{y_3}{x_3}[/tex]
Option 2 is incorrect.
In table 3,
[tex]\frac{y_1}{x_1}=\frac{2}{1}[/tex]
[tex]\frac{y_2}{x_2}=\frac{3}{2}[/tex]
[tex]\frac{y_1}{x_1}\neq \frac{y_2}{x_2}[/tex]
Option 3 is incorrect.
In table 4,
[tex]\frac{y_1}{x_1}=\frac{2}{1}=2[/tex]
[tex]\frac{y_2}{x_2}=\frac{4}{2}=2[/tex]
[tex]\frac{y_3}{x_3}=\frac{6}{3}=2[/tex]
[tex]\frac{y_}{x_1}=\frac{y_2}{x_2}=\frac{y_3}{x_3}[/tex]
Option 4 shows a possible ratio table for ingredients X and Y for the given number of servings.
Therefore the correct option is 4.
