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 [tex]*[/tex] 80 solution, as 0.70 is associated with 80. Therefore we can formulate the following expression,
0.40x + 0.80y = 0.70 [tex]*[/tex] 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.
[tex]0.40\left(\:80\:-\:y\:\right)\:+\:0.80y\:=\:0.70\:\cdot \:80[/tex]
[tex]0.4\left(80-y\right)+0.8y=56[/tex] ( Multiply either side by 10 )
[tex]4\left(80-y\right)+8y=560[/tex] ( Expand )
[tex]320-4y+8y=560[/tex]
[tex]320+4y=560[/tex]
[tex]4y=240[/tex]
[tex]y = \frac{240}{4} = 60[/tex] ( Substitute to solve for x )
[tex]x = 80 - y = 80 - 60 = 20[/tex]
As you can see there are 20 gallons of the 40% solution, and 60 gallons of the 80% solution.
