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} \\ =(45)/(100)* X=0.45X \end{gathered}`

The second brand is 70% pure antifreeze, this implies

`\begin{gathered} 70\text{ percent of X} \\ =(70)/(100)* 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=(65)/(100)* X \\ 50=0.65X \\ X=(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*76.923=34.615`

Second brand:

`0.70X=0.70*76.923=53.846`

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