A 50% antifreeze solution is to be mixed with an 80% antifreeze solution to get 180 liters of a 75% solution. How many liters of the 50% solution and how many liters of the 80% solution will be used?

Step-by-step explanation:

If x is the volume of 50% solution and y is the volume of 80% solution, then the total volume is:

x + y = 180

And the total amount of antifreeze is:

0.50 (x) + 0.80 (y) = 0.75 (180)

0.5x + 0.8y = 135

Solving the system of equations:

0.5x + 0.8 (180 - x) = 135

0.5x + 144 - 0.8x = 135

9 = 0.3x

x = 30

y = 180 - x

y = 150

You need 30 gallons of 50% solution and 150 gallons of 80% solution.