Question 531060
The chemist needs 100 ml of a 20% solution.
.2*100 ml = 20 ml of pure iodine in the 100 ml solution.
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The chemist has 10% solution and 50% solution.
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x = 10% solution
y = 50% solution
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x + y = 100 ml
x = 100-y ml
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.1x + .5y = .2*100
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multiply by 10 to eliminate the decimals
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1*x + 5*y = 2*100
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substitute
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(100-y) + 5y = 200
100 + 4y = 200
4y = 100
y = 25 ml of 50% iodine
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x = 100-25
x = 75 ml of 10% iodine
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Check the amount of pure stuff to be sure this is the answer.
.5*25 = 12.5 ml
.1*75 = 7.5 ml
12.5 + 7.5 = 20 ml, which is the amount we need.
Correct.
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Done.