How many gallons?

Question

How many gallons of 25% alcohol solution and 45% alcohol solution must be mixed to get 16 gallons of 35% alcohol solution? There needs to be x gallons of 25% alcohol solution and x gallons of 45% solution.

Answer 1

First off, we need to create to equations; one for volume and one to account for the volume and strength.

 

Eq 1) x + y = 16 gallons → y= 16 - x

 

Eq 2) 0.25x + 0.45y = 16*0.35

 

Since we rearranged Eq 1, we can now substitute the y as 16 -x in Eq 2.

 

 0.25x + 0.45 (16-x)= 5.6

 

0.25x + 7.2 - 0.45x= 5.6

-0.2x = -1.6

 

x= 8 gallons

 

To find y, plug the x value of 8 into Eq 1.