how many gallons of a 24%-alcohol solution must be mixed with a 52%-alcohol solution to obtain 40 gallons of a 36.25 alcohol solution?

Question

how many gallons of a 24%-alcohol solution must be mixed with a 52%-alcohol solution to obtain 40 gallons of a 36.25 alcohol solution?

Answer 1

 

Hi Natalie,

 

Let x and y represent how many gallons of a 24%- and

 

a 52%-alcohol solution to be used, respectively.

 

Then, we get a set of linear equations as follows.

 

     x + y = 40     (as the resulting solution is 40 gallons in total)

 

     0.24x + 0.52y = 0.3625·40     (from the amount of alcohol itself)

 

By solving the set of equations above,

 

we get x = 22.5 and y = 17.5.

 

So, we can get 40 gallons of a 36.25%-alcohol solution

 

by mixing 22.5 gallons of a 24%-alcohol solution

 

with 17.5 gallons of a 52%-alcohol solution.