Mixture problem

Question

how many ounces of a 30% alcohol must be mixed with 14 ounces of a 35% solution to make a 32%  alcohol  solution? 

Answer 1

Since you are given that you will end up with a certain unknown amount of a 32% solution, your equation will be based on actual amount of alcohol in the various solutions.

 

Let y = the amount of 30% solution we will need.

 

0.35 x 14 is the expression for the amount of alcohol in the 14 oz of 35% solution

0.3y is the expression for the amount of alcohol in the 30% solution

The final 32% solution contains 0.32(y + 14) oz of alcohol

 

Therefore,

 

0.35(14) + 0.3y = 0.32(14 + y)

 

4.9 + 0.3y = 4.48 + 0.32y

0.42 = 0.02y (subtract 4.48 from both sides, subtract 0.3 y from both sides)

21 = y (diving both sides by 0.02)

 

Reality check:  If we mixed equal amounts (i.e., 14 oz) of the 30% and 35% solutions, we would come out with a 32.5% solution.  But we want the solution to be less concentrated, so we will need more than 14 oz of the 30% solution, which meshes with our answer.