Answer
The function of x is given by the following equation:
$S\left( x \right)=30-\frac{x}{2}$
Work Step by Step
The value of function is $S\left( 30 \right)=15$ mL
The amount of sodium iodine in milliliters due to $10\%$ sodium-iodine solution in the mixture is as follows
$\begin{align}
& {{S}_{1}}\left( x \right)=\frac{10}{100}x \\
& =\frac{x}{10}
\end{align}$
The amount of $60\%$ sodium-iodine solution in the mixture is $\left( 50-x \right)$ mL.
The amount of sodium iodine in milliliters due to $60\%$ sodium-iodine solution in the mixture is
$\begin{align}
& {{S}_{1}}\left( x \right)=\frac{60}{100}\left( 50-x \right) \\
& =\frac{\left( 300-6x \right)}{10}
\end{align}$
The function for total amount of sodium iodine in milliliters in the mixture is
$\begin{align}
& S\left( x \right)={{S}_{1}}\left( x \right)+{{S}_{2}}\left( x \right) \\
& =\frac{x}{10}+\frac{\left( 300-6x \right)}{10} \\
& =\frac{300-5x}{10} \\
& =30-\frac{x}{2}
\end{align}$
Put $x=30$ in the function to calculate the value of $S\left( 30 \right)$:
$\begin{align}
& S\left( 30 \right)=30-\frac{30}{2} \\
& =15
\end{align}$
Thus, the total amount of sodium iodine is written as a function of x and $S\left( 30 \right)$ is evaluated.
