Solving a linear equation, we can see that you need to use 300 gallons of the 50% antifreeze.
How many gallons of each antifreeze should we use?
We want to make a 40% antifreeze.
Let's define x as the number of gallons of the 50% antifreeze that we will use, and we will mix that with 100gal of 10% antifreeze, then the total volume will be:
x + 100
And the concentration must be 40% (or 0.4 in decimal form), then the concentrations in the left must be the same as the one in the right:
x*0.5 + 100*0.1 = (x + 100)*0.4
This is just a linear equation that we can solve to find the value of x:
x*0.5 + 10 = x*0.4 + 40
x*0.5 - x*0.4 = 40 - 10
x*0.1 = 30
x = 30/0.1 = 300
This means that you need to use 300 gallons of the 50% antifreeze.
If you want to learn more about linear equations:
https://brainly.com/question/1884491
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