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-.)A chemical company makes two brands of antifreeze. The first brand is 65 % pure antifreeze, and the second brandis 95 % pure antifreeze. In order to obtain 120 gallons of a mixture that contains 70% pure antifreeze, how manygallons of each brand of antifreeze must be used?First brand:Second brand:

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SOLUTION

let the first brand be taken as x

And the second be taken as y. So

[tex]\begin{gathered} x+y=120\text{ gallons } \\ y=120-x \end{gathered}[/tex]

For their percentage purity to make up 120 gallons at 70%, we have

[tex]\begin{gathered} x(\frac{65}{100})+y(\frac{95}{100})=120(\frac{70}{100}) \\ x(0.65)+y(0.95)=120(0.7) \\ x(0.65)+(120-x)(0.95)=120(0.7) \\ 0.65x+114-0.95x=84 \\ 114-84=0.95x-0.65x \\ 30=0.3x \\ x=\frac{30}{0.3} \\ x=100 \end{gathered}[/tex]

So, y becomes

[tex]\begin{gathered} y=120-x \\ y=120-100 \\ y=20 \end{gathered}[/tex]

Hence the first brand is 100 gallons

And the second brand is 20 gallons

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