document.write( "Question 531060: A Chemist has a mixture that is 10% iodine and another that is 50% iodine. How much of each solution should the druggist use to get 100 ml of a solution that is 20% iodine \n" ); document.write( "

Algebra.Com's Answer #350324 by oberobic(2304) $\"\"$ $\"About$

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

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