SOLUTION: A bartender needs to make 5 gallons of a mixed drink containing 12% alcohol. she is going to combine a 10% with a 15% alcohol. how much of each should she use?

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Question 1088063: A bartender needs to make 5 gallons of a mixed drink containing 12% alcohol. she is going to combine a 10% with a 15% alcohol. how much of each should she use?
Found 2 solutions by Tatiana_Stebko, MathTherapy:
Answer by Tatiana_Stebko(1539) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the number of gallons with a 10% alcohol
Let y be the number of gallons with a 15% alcohol
A bartender needs to make 5 gallons of a mixed drink => x%2By=5
a mixed drink contains 12% alcohol => 0.10x%2B0.15y=0.12%2A5
The system of equations
system%28x%2By=5%2C+0.10x%2B0.15y=0.6%29
Multiply the second equation by 10
system%28x%2By=5%2C+x%2B1.5y=6%29
system%28x=5-y%2C+x%2B1.5y=6%29
substitute x=5-y into the second equation
system%28x=5-y%2C+5-y%2B1.5y=6%29
system%28x=5-y%2C+0.5y=1%29
system%28x=5-y%2C+y=2%29
system%28x=5-2%2C+y=2%29
system%28x=3%2C+y=2%29
A bartender needs to combine 3 gallons with a 10% alcohol and 2 gallons with a 15% alcohol

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

A bartender needs to make 5 gallons of a mixed drink containing 12% alcohol. she is going to combine a 10% with a 15% alcohol. how much of each should she use?
Let amount of 10% alcohol to mix, be T

Then amount of 15% alcohol needed = 5 - T

We then get the following MIXTURE equation: .1T + .15(5 - T) = .12(5)

.1T + .75 - .15T = .6

.1T - .15T = .6 - .75

- .05T = - .15

T, or