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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?

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MathPhys

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.

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