Achemical company makes two brands of antifreeze. the first brand is 20% pure antifreeze, and the second brand is 70% pure antifreeze. in order to obtain 30 gallons of a mixture that contains 35% pure antifreeze, how many gallons of each brand of antifreeze must be used?

First brand of antifreeze: 21 gallons

Second brand of antifreeze: 9 gallons

Step-by-step explanation:

Let's call A the amount of  first brand of antifreeze. 20% pure antifreeze

Let's call B the amount of second brand of antifreeze. 70% pure antifreeze

The resulting mixture should have 35% pure antifreeze, and 30 gallons.

Then we know that the total amount of mixture will be:

Then the total amount of pure antifreeze in the mixture will be:

Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -0.7 and add it to the second equation:

               +

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We substitute the value of A into one of the two equations and solve for B.