Word Problem

Question

doreen is a chemist. she needs to prepare 28 ounces of a 11% acid solution. find the amount of 14% solution and the amount of 7% solution she should mix to get this solution

how many ounces of the 14% solution should be in the mixture?
how many ounces of the 7% solution should be in the mixture?

Answer 1

The formula to solve this problem is C1V1 + C2V2 = C3V3
This problem is a dilution of the 14% solution by adding enough of the 7% solution to total 28oz at 11%
 
So, let x = the amount of the 7% solution, or C1V1 = 7%x
Then the amount of the 14% solution will be 28oz -x times its concentration, so 14%(28oz-x)
 
the two amounts will total 28oz·11%
 
Our formula will be 7%x + 14%(28oz-x) = 11%28oz
 
to make the formula easier to use, we will convert the % to decimals, so 7% = 0.07, 11% = 0.11, and 14% = 0.14
 
the formula becomes 0.07x + 0.14(28oz - x) = 0.11·28oz
expanding, we get 0.07x + 3.92oz - 0.14x = 3.08oz
combining terms, we get 3.92oz - 3.08oz = -0.07x; -0.84oz = -0.07x; x = 12oz
 
So, 12oz of the 7% solution will be used to dilute 16oz of the 14% solution.
 
Proof: 12 x 0.07 + 16 x .04 = 28 x 11; 3.08 = 3.08