SOLUTION: 5. Translate the problem into a pair of linear equations in two vaiables. Solve the equations using either elimination or substitution. State your answer for the specified variable

Question 231351: 5. Translate the problem into a pair of linear equations in two vaiables. Solve the equations using either elimination or substitution. State your answer for the specified variable.
How many liters of a 40%-alcohol solution must be mixed with 10 liters of a solution that is 80% alcohol to get a solution that is 60% alcohol?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
How many liters of a 40%-alcohol solution must be mixed with 10 liters of a solution that is 80% alcohol to get a solution that is 60% alcohol?
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Quantity Eq:: x + 10 = y
Alcohol Eq:::0.4x + 0.8*10 = 0.6y
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Rearrange:
y - x = 10
0.6y -0.4x = 0.8*10
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Multiply thru 1st by 6 ; Multiply thru 2nd by 10
6y - 6x = 60
6y - 4x = 80
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Subtract 1st from 2nd to get:
2x = 20
x = 10 liters (amt of 40% solution in the mixture)
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Since y = x+10, y = 20 liters (amt of 60% solution in the mixture)
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Cheers,
Stan H.
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