Achemical company makes two brands of antifreeze. the first brand is 60% pure antifreeze, and the second brand is 90% pure antifreeze. in order to obtain 180 gallons of a mixture that contains 85% pure antifreeze, how many gallons of each brand of antifreeze must be used?

30 gallons of the first brand and 150 gallons of the second one.

Explanation:

We have two unknown quantities, and , so it is necessary to write two equations that relate that variables. First, we are going to consider that the volume is an additive property, which means that if you mix and gallons the final volume V will be:

The other equation we will write is based on a mass balance of the antifreeze. We know that the content of antifreeze in a given volume is the multiplication of that volume by the concentration, so the mass balance would be:

It means that the total of the antifreeze in the final mix (which is ) is equal to the sum of the antifreeze that was on the first brand volume (V_1*x_1) and the antifreeze that was on the second brand volume (V_2*x_2).

Now we have a two equation two unknown system, so let's solve it:

From first equation:

,

Replace on the second one.

Finally, from ,

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