Question

A container holds 100 ml of a solution that is 25 ml acid. If n ml of a solution that is 60% acid is added, the function C(n) = 25 + 0.6n/100 + n gives the concentration, C, as a function of the number of ml added, n. Express n as a function of C and determine the number of mL that need to be added to have a solution that is 50% acid.

For the above exercises, determine the function described and then use it to answer the question.

Answer 1

Function for concentration is C(n) = (25 + .6n)/(100 + n), where n is the number of mL added.

n as a function of concentration, C:

First replace the function with variable C

C = (25 + .6n)/(100 + n)

 

Now solve for n:

Multiply both sides by 100 + n

 

C(100 + n) = 25 + .6n

100C + Cn = 25 + .6n

    Cn - .6n = 25 – 100C

 

Take n common

n(C - .6) = 25 – 100C

           n = (25 – 100C)/(C - .6)

 

So, n = (25 – 100C)/(C - .6)

 

To find the number of mL added to have a solution that is 50% acid:

Put C = 0.5 in the obtained equation:

n = {25 – 100(0.5)}/(0.5 - .6)

   = (25 – 50)/-0.1

   = -25/-0.1

   = 250

So, to have a solution that is 50% acid, number of mL to be added is 250.

So, to have a solution that is 50% acid, number of mL to be added is 250.