Answer:
20 gallons of the 40% solution, 60 gallons of the 80% solution
Step-by-step explanation:
Let x = the gallons of the 40% solution, and y = the gallons of a 80% solution. The first thing we want to do here is to convert each percentage into decimal form - including the 70% solution mixture.
40% = 0.40,
80% = 0.80, respectively 70% = 0.70
As you can tell, 0.40 is associated with x gallons, 0.80 is associated with y gallons, and the mixture contains 0.70
80 solution, as 0.70 is associated with 80. Therefore we can formulate the following expression,
0.40x + 0.80y = 0.70
80
At the same time x + y = 80, as the solution ( mixture ) is present with 80 gallons. Isolating x, x = 80 - y. Let us plug that into our expression, solving for y, following by x gallons.
![0.40\left(\:80\:-\:y\:\right)\:+\:0.80y\:=\:0.70\:\cdot \:80](https://tex.z-dn.net/?f=0.40%5Cleft%28%5C%3A80%5C%3A-%5C%3Ay%5C%3A%5Cright%29%5C%3A%2B%5C%3A0.80y%5C%3A%3D%5C%3A0.70%5C%3A%5Ccdot%20%5C%3A80)
( Multiply either side by 10 )
( Expand )
![320-4y+8y=560](https://tex.z-dn.net/?f=320-4y%2B8y%3D560)
![320+4y=560](https://tex.z-dn.net/?f=320%2B4y%3D560)
![4y=240](https://tex.z-dn.net/?f=4y%3D240)
( Substitute to solve for x )
![x = 80 - y = 80 - 60 = 20](https://tex.z-dn.net/?f=x%20%3D%2080%20-%20y%20%3D%2080%20-%2060%20%3D%2020)
As you can see there are 20 gallons of the 40% solution, and 60 gallons of the 80% solution.