Alcohol Solutions

Question

A nurse needs rubbing alcohol, which is a 70% alcohol solution. However, there is only a 40% alcohol solution and a 90% alcohol solution in stock. How much of each solution should be mixed in order to obtain 8 ounces of the desired 70% solution?

Answer 1

Let X and Y be the amounts of the 40-proof and 90-proof alcohol solutions respectively.

 

The amount of alcohol is:

 

  0.4*X + 0.9*Y = 0.7 * 8

 

The total amount of ounces is X + Y = 8

 

Solving the second equation for Y and multiplying the first equation by 10 to clear the decimals,

the system becomes:

 

Y  =  8   -  X

 

4X +9Y = 56

 

 

Substuting :

 

4X + 9( 8 - X ) = 56

 

4X + 72 - 9X = 56

 

72 - 5X = 56

 

72 - 5X - 56 = 0

 

16 - 5X = 0

 

16 = 5X

 

X = 16/5 = 3 and 1/5 = 3.2

 

Y = 8 - 3.2 = 4.8

 

 

 

CHECK: 0.4 * 3.2 + .9 * 4.8 = 5.6 = .7 x 8

 

3.2 ounces of the 40-proof and 4.8 ounces of the 90 proof.