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Alcohol Solutions

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?
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1 Answer

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.
               
 
 

Comments

Give me a double shot of the 90 proof please.  :-)