Question

A chemical company makes two brands of antifreeze. The first brand is 30 pure antifreeze, and the second brand is 80 pure antifreeze. In order to obtain 150 gallons of a mixture that contains 40 pure antifreeze, how many gallons of each brand of antifreeze must be used?

Answer 1

Answer: Let x be the number of gallons of the first brand (30% pure antifreeze) that needs to be mixed, and let y be the number of gallons of the second brand (80% pure antifreeze) that needs to be mixed. We want to find the values of x and y that satisfy the following conditions:

The total amount of antifreeze mixed is 150 gallons: x + y = 150

The resulting mixture is 40% pure antifreeze: 0.3x + 0.8y = 0.4(150)

We have two equations with two unknowns, so we can solve for x and y. We'll use the first equation to solve for y in terms of x:

y = 150 - x

Substituting this expression into the second equation gives:

0.3x + 0.8(150 - x) = 60

Simplifying and solving for x:

0.3x + 120 - 0.8x = 60

-0.5x = -60

x = 120

Substituting this value back into y = 150 - x gives:

y = 150 - 120 = 30

Therefore, we need to mix 120 gallons of the first brand and 30 gallons of the second brand to obtain 150 gallons of a mixture that contains 40% pure antifreeze.

Explanation: