Question

A chemical company makes two brands of antifreeze. The first brand is 45% pure antifreeze, and the second brand is 70% pure antifreeze. In order to obtain 50gallons of a mature that contains 65% pure antifreeze, how many gallons of each brand of antifreeze must be used?

Answer 1

Let the amount of antifreeze be represented as X

The first brand is 45% pure antifreeze, this implies

$\begin{gathered} 45\text{ percent of X} \\ =\frac{45}{100}\times X=0.45X \end{gathered}$

The second brand is 70% pure antifreeze, this implies

$\begin{gathered} 70\text{ percent of X} \\ =\frac{70}{100}\times X=0.70X \end{gathered}$

Since 50 gallons of the mixture contains 65% pure antifreeze, this implies

$\begin{gathered} 50=65\text{ percent of X} \\ 50=\frac{65}{100}\times X \\ 50=0.65X \\ X=\frac{50}{0.65}=76.923 \end{gathered}$

Thus, the amount of antifreeze is 76.923.

To determine the amount of antifreeze in each brand, we have

First brand:

$0.45X=0.45\times76.923=34.615$

Second brand:

$0.70X=0.70\times76.923=53.846$

Hence, the first and second brands contain 34.615 and 53.846 gallons of antifreeze respectively.