Answer:
30x - 18
Step-by-step explanation:
6(5x - 3)
Apply the distributive property.
6(5x) + 6(-3)
30x + - 18
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:
![A + B = 30](https://tex.z-dn.net/?f=A%20%2B%20B%20%3D%2030)
Then the total amount of pure antifreeze in the mixture will be:
![0.2A + 0.7B = 0.35 * 30](https://tex.z-dn.net/?f=0.2A%20%2B%200.7B%20%3D%200.35%20%2A%2030)
![0.2A + 0.7B = 10.5](https://tex.z-dn.net/?f=0.2A%20%2B%200.7B%20%3D%2010.5)
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:
![-0.7A -0.7B = -0.7*30](https://tex.z-dn.net/?f=-0.7A%20-0.7B%20%3D%20-0.7%2A30)
![-0.7A -0.7B = -21](https://tex.z-dn.net/?f=-0.7A%20-0.7B%20%3D%20-21)
![-0.7A -0.7B = -21](https://tex.z-dn.net/?f=-0.7A%20-0.7B%20%3D%20-21)
+
![0.2A + 0.7B = 10.5](https://tex.z-dn.net/?f=0.2A%20%2B%200.7B%20%3D%2010.5)
--------------------------------------
![-0.5A = -10.5](https://tex.z-dn.net/?f=-0.5A%20%3D%20-10.5)
![A = \frac{-10.5}{-0.5}](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B-10.5%7D%7B-0.5%7D)
![A = 21\ gallons](https://tex.z-dn.net/?f=A%20%3D%2021%5C%20gallons)
We substitute the value of A into one of the two equations and solve for B.
![21 + B = 30](https://tex.z-dn.net/?f=21%20%2B%20B%20%3D%2030)
![B = 9\ gallons](https://tex.z-dn.net/?f=B%20%3D%209%5C%20gallons)
It's out of B, D. I did this last year, but it's definitely out of those two choices.
Answer:
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