Question 519758
When doing mixture or solution problems, focus on how much 'pure' stuff you need.
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10 liters of 40% disinfectant will have 10*.4 = 4.0 liters of pure disinfectant and 6.0 liters of water (or some other solvent).
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x = liters of 75% solution to use
y = liters of 25% solution to use
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however, we know
x + y = 10
so
y = 10-x
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That approach means we have only one unknown and, therefore, only need one equation to solve it.
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.75*x + .25(10-x) = .40(10)
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multiply through by 100 to eliminate the decimals
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75x + 25(10-x) = 40(10)
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75x + 250 - 25x = 400
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50x = 150
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x = 3
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y = 10-3
y = 7
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Answer: Mix 3 liters of 75% disinfectant with 7 liters of 25% disinfectant to produce 10 liters of 40% solution.
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Check the answer by checking how much pure stuff you have.
.75*3 = 2.25
.25*7 = 1.75
2.25 + 1.75 = 4.00 liters of pure disinfectant in the 10 liters, which is a 40% solution.
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Done.