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How many gallons each of 15% alcohol and 10% alcohol should be mixed to obtain 5 gal of 11% alcohol?

How many gallons of 15% alcohol should be in the mixture

How many gallons of 10% alcohol should be in the mixture

User Silkster
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1 Answer

1 vote

Answer:

Explanation:

Let x be the number of gallons of 15% alcohol needed.

Then the number of gallons of 10% alcohol needed is 5 - x.

The amount of pure alcohol in x gallons of 15% alcohol is 0.15x, and the amount of pure alcohol in 5 - x gallons of 10% alcohol is 0.1(5 - x).

To obtain 5 gallons of 11% alcohol, the amount of pure alcohol in the mixture must be:

0.11(5) = 0.15x + 0.1(5 - x)

Simplifying and solving for x, we get:

0.55 = 0.05x + 0.5 - 0.1x

0.55 = 0.5 - 0.05x

0.05x = 0.05

x = 1

Therefore, we need 1 gallon of 15% alcohol and 4 gallons of 10% alcohol to obtain 5 gallons of 11% alcohol.

To answer the additional questions:

The mixture contains 1 gallon of 15% alcohol.

The mixture contains 4 gallons of 10% alcohol.

User Bhrungarajni
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