Final answer:
To solve for the amount of 90% antifreeze solution needed, we set up an equation using weighted averages in solutions, resulting in 300 gallons, which is not among the options provided.
Step-by-step explanation:
To determine how many gallons of a 90% antifreeze solution must be mixed with 60 gallons of 20% antifreeze to get a mixture that is 80% antifreeze, we can use the concept of weighted averages in solutions. The total amount of antifreeze in the final solution should be equal to the sum of the antifreeze in the individual solutions before mixing.
Let x represent the number of gallons of the 90% solution. The total amount of pure antifreeze from the 90% solution is 0.90x gallons, and the total from the 60 gallons of 20% solution is 0.20 * 60 gallons. Since we want to have an 80% solution after mixing, the equation to solve is:
0.90x + 0.20(60) = 0.80(x + 60)
Solving this equation gives us:
0.90x + 12 = 0.80x + 48
0.10x = 36
x = 36 / 0.10
x = 360 gallons
However, we need to remember that x is the total amount of the mixed solution, not just the amount of the 90% solution added. Since 60 gallons of the 20% solution are already there, we subtract 60 from our result:
360 gallons - 60 gallons = 300 gallons
Therefore, 300 gallons of a 90% antifreeze solution must be mixed with 60 gallons of 20% antifreeze to achieve an 80% antifreeze solution. Since 300 is not one of the provided options, there might have been a misunderstanding in the question or the provided choices.