Example 2.2.1.
Suppose we have a container with a solution of sugar water that is 22% sugar and another container with a solution of sugar water that is 16% sugar. If we combine 150 g of the first solution and 250 g of the second solution, what is the percent of sugar in the resulting solution? Round the percent to two decimal places.
To calculate a percent we need the amount of the part and the amount of the whole. We are told the total amount of each solution we are using, so we can calculate the whole (total amount of resulting solution) directly. Because they have the same units we can add.
\begin{equation*}
T=150 \text{ g}+250 \text{ g}=400 \text{ g}\text{.}
\end{equation*}
We cannot simply add the amounts of sugar from each because we are told the percent rather than the amount. However, we know how to convert a percent and total amount to an amount of the part. We did this in Example 2.1.5.
\begin{align*}
S_1 & = 150 \text{ g} \cdot 0.22\\
& = 33 \text{ g}\\
S_2 & = 250 \text{ g} \cdot 0.16\\
& = 40 \text{ g}\text{.}
\end{align*}
\begin{align*}
P & = 33 \text{ g}+40 \text{ g}\\
& = 73 \text{ g}\text{.}
\end{align*}
Finally we can calculate the percent of sugar in the resulting mixture using the defintion of percent. The percent of sugar in the resulting mixture is
\begin{equation*}
\frac{\text{Part}}{\text{Whole}} = \frac{73 \text{ g}}{400 \text{ g}} = 0.1825 = 18.25\%\text{.}
\end{equation*}
