A chemist wishes to mix a solution that is 8​% acid..

Question

A chemist wishes to mix a solution that is 8% acid. She has on hand 10 liters of a 4% acid solution and wishes to add some 12% acid solution to obtain the desired 8% acid solution. How much 12% acid solution should she add?

(I'm trying to figure this problem out)

Complete The Table.

Liters of                         Percent Acid                   Liters of Pure
Solution                        (As A Decimal)                       Acid

10                                     0.04                                 [ ? ] 
x                                       0.12                                 [ ? ]
[ ? ]                                   0.08                                [ ? ]

Answer 1

Assuming she wants to use all 10 liters of the 4% acid, you can set up the solution as follows:

 

x = required liters of the 12% acid

 

(4%)(10) + (12%)x = (8%)(x + 10)

 

4(10) + 12x = 8(x + 10)

 

Solve for x and get

 

x = 10 liters

 

Note that it makes sense to mix as much of the 12% as the 4% since the target mixture of 8% is midway between 4% and 12%.