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: