Question

SHALL GIVE BRAINLIEST ANSWER!! A ​40% solution of fertilizer is to be mixed with an ​80% solution of fertilizer in order to get 80 gallons of a ​70% solution. How many gallons of the ​40% solution and ​80% solution should be​ mixed? 40% solution =? gallons, 80% solution =? gallons

Answer 1

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.

$0.40\left(\:80\:-\:y\:\right)\:+\:0.80y\:=\:0.70\:\cdot \:80$

$0.4\left(80-y\right)+0.8y=56$ ( Multiply either side by 10 )

$4\left(80-y\right)+8y=560$ ( Expand )

$320-4y+8y=560$

$320+4y=560$

$4y=240$

$y = \frac{240}{4} = 60$ ( Substitute to solve for x )

$x = 80 - y = 80 - 60 = 20$

As you can see there are 20 gallons of the 40% solution, and 60 gallons of the 80% solution.