Answer:
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:
[tex]A + B = 30[/tex]
Then the total amount of pure antifreeze in the mixture will be:
[tex]0.2A + 0.7B = 0.35 * 30[/tex]
[tex]0.2A + 0.7B = 10.5[/tex]
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:
[tex]-0.7A -0.7B = -0.7*30[/tex]
[tex]-0.7A -0.7B = -21[/tex]
[tex]-0.7A -0.7B = -21[/tex]
+
[tex]0.2A + 0.7B = 10.5[/tex]
--------------------------------------
[tex]-0.5A = -10.5[/tex]
[tex]A = \frac{-10.5}{-0.5}[/tex]
[tex]A = 21\ gallons[/tex]
We substitute the value of A into one of the two equations and solve for B.
[tex]21 + B = 30[/tex]
[tex]B = 9\ gallons[/tex]
