You mix a 75% acid solution with a 25% acid solution how many liters of each were used to make 20 liters of a 40% acid solution

Question

Cant figure this out!

Answer 1

Hi Rob,

 

Let's begin by assigning letters to represent our unknown quantities:

 

x = volume (liters) of 75% acid solution used

y = volume (liters) of 25% acid solution used

 

Now let's come up with two equations which we can use to solve for our two unknowns:

 

Equation #1:  0.75x + 0.25y = 0.40(20)

Equation #2:  x + y = 20

 

Equation #1 expresses the individual concentrations of acid combined to make up the final concentration of acid.

 

Equation #2 expresses the individual amounts of solution combined to make up the final amount of solution.

 

Now let's express one of the unknowns in terms of the other unknown using Equation #2 (we'll express y in terms of x):

    x + y =20 (Equation #2)

          y = 20 - x

 

Let's use our expression for y in terms of x and plug it into Equation #1 and solve for x:

    0.75x + 0.25y = 0.40(20)  [Equation #1)

    0.75x + 0.25(20 - x) = 0.40(20)

    0.75x + 5 - 0.25x = 8

    0.75x - 0.25x = 8 - 5

    0.5x = 3

        x = 6 (liters of 75% acid solution used)

 

Now let's use Equation #2 to solve for y (plugging in our value of 6 for x):

    x + y = 20 (Equation #2)

    6 + y = 20

          y = 20 - 6

          y = 14 (liters of 25% acid solution used) 

 

Finally, let's check our answers by plugging both our values for x and y into Equation #1 and see if both sides match:

    0.75x + 0.25y = 0.40(20)  [Equation #1]

    0.75(6) + 0.25(14) = 0.40(20)

    4.5 + 3.5 = 8

               8 = 8 (both sides match)

 

As we can see, both sides match, so we are confident that our values for x and y are indeed correct.

 

Thanks for submitting this problem and glad to have been of help.

 

God bless, Jordan.