document.write( "Question 511931: How many liters of a mixture containing 70% alcohol should be added to a mixture containing 20% alcohol to obtain 16 liters of a mixture containing 50% alcohol? \n" ); document.write( "

Algebra.Com's Answer #342458 by oberobic(2304) $\"\"$ $\"About$

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To do mixture problems you need to keep track of how much 'pure' stuff you have or need.
\n" ); document.write( "In 16 liters of a 50% alcohol solution, you have .5*16 = 8 liters of 'pure' alcohol.
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\n" ); document.write( "Since you have a defined amount to make, you can define your variables as follows:
\n" ); document.write( "x = amount of 70% alcohol to add
\n" ); document.write( "(16-x) = the amount of 20% alcohol to add
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\n" ); document.write( "70%*x + 20%*(16-x) = 50%*16
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\n" ); document.write( ".7x + .2(16-x) = 8
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\n" ); document.write( "multiply by 10 to eliminate decimals
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\n" ); document.write( "7x + 2(16-x) = 80
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\n" ); document.write( "7x + 32 -2x = 80
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\n" ); document.write( "5x = 48
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\n" ); document.write( "x = 48/5 = 9 3/5
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\n" ); document.write( "16-x = 80/5 - 48/5 = 32/5 = 6 2/5
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\n" ); document.write( "So, you add 9 3/5 liters of of 70% and 6 2/5 liters of 20% to produce 16 liters of 50% alcohol.
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\n" ); document.write( "Check the amount of 'pure' stuff to be sure this answer is correct.
\n" ); document.write( ".7*48/5 = 6.72
\n" ); document.write( ".2*32/5 = 1.28
\n" ); document.write( "6.72 + 1.28 = 8, which we know is the right answer from the first step.
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\n" ); document.write( "Done. \n" ); document.write( "

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