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?

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.**

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