Question

A chemical company makes two brands of antifreeze. The first brand is 55% pure antifreeze, and the second brand is 70% pure antifreeze. In order to obtain 60 gallons of a mixture that contains 60% pure antifreeze, how many gallons of each brand of antifreeze must be used?

Answer 1

Let's denote the amount of the first brand antifreeze as "x" gallons and the amount of the second brand antifreeze as "60 - x" gallons. We want to find the values of "x" and "60 - x" that will result in a mixture of 60 gallons with a purity of 60% antifreeze.

The equation to represent the mixture's purity is:

(55% * x) + (70% * (60 - x)) = 60% * 60

Now let's solve for "x":

0.55x + 0.70(60 - x) = 0.60 * 60

0.55x + 42 - 0.70x = 36

-0.15x = -6

x = 6 / 0.15

x = 40

So, you would need 40 gallons of the first brand antifreeze (55% pure) and 20 gallons of the second brand antifreeze (70% pure) to obtain 60 gallons of a mixture containing 60% pure antifreeze.