document.write( "Question 170410: I get really confused when trying to set these problems up. Can you help me work this one out so I can use it for my other questions please? How many liters of a 40% alcohol solution should be mixed with 40 liters of a 90% solution to get a 50% solution? Thanks for your help. \n" ); document.write( "

Algebra.Com's Answer #125811 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!
Edwin's solution with chart:
\n" ); document.write( "I get really confused when trying to set these problems up. Can you help me work this one out so I can use it for my other questions please? How many liters of a 40% alcohol solution should be mixed with 40 liters of a 90% solution to get a 50% solution? Thanks for your help.
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document.write( "Make this chart:\r\n" );
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document.write( "               | liters |  %  | pure alcohol\r\n" );
document.write( "--------------------------------------------\r\n" );
document.write( "1st solution   |        |     |           \r\n" );
document.write( "2nd solution   |        |     |            \r\n" );
document.write( "---------------|--------|-----|-------------\r\n" );
document.write( "final solution |        |     |          \r\n" );
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document.write( "Let x = liters of 1st solution\r\n" );
document.write( "and we are given that there are 40 liters\r\n" );
document.write( "of the 2nd solution, so fill in x and 40 \r\n" );
document.write( "liters.\r\n" );
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document.write( "               | liters |  %  | pure alcohol\r\n" );
document.write( "--------------------------------------------\r\n" );
document.write( "1st solution   |    x   |     |      \r\n" );
document.write( "2nd solution   |   40   |     |    \r\n" );
document.write( "---------------|--------|-----|-------------\r\n" );
document.write( "final solution |        |     |\r\n" );
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document.write( "Add the two to get x+40 liters of final solution.\r\n" );
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document.write( "               | liters |  %  | pure alcohol\r\n" );
document.write( "--------------------------------------------\r\n" );
document.write( "1st solution   |    x   |     |      \r\n" );
document.write( "2nd solution   |   40   |     |   \r\n" );
document.write( "---------------|--------|-----|-------------\r\n" );
document.write( "final solution | x+40   |     | \r\n" );
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document.write( "Put in the three percentages as decimals:\r\n" );
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document.write( "               | liters |  %  | pure alcohol\r\n" );
document.write( "--------------------------------------------\r\n" );
document.write( "1st solution   |    x   | .40 |      \r\n" );
document.write( "2nd solution   |   40   | .90 |     \r\n" );
document.write( "---------------|--------|-----|-------------\r\n" );
document.write( "final solution | x+40   | .50 | \r\n" );
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document.write( "Now get the amount of pure alcohol contained\r\n" );
document.write( "in each by multiplying by the percentage as\r\n" );
document.write( "a decimal.\r\n" );
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document.write( "               | liters |  %  | pure alcohol\r\n" );
document.write( "--------------------------------------------\r\n" );
document.write( "1st solution   |    x   | .40 |      .40x\r\n" );
document.write( "2nd solution   |   40   | .90 |   .90(40)  \r\n" );
document.write( "---------------|--------|-----|-------------\r\n" );
document.write( "final solution | x+40   | .50 | .50(x+40)\r\n" );
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document.write( "The equation comes from the last column:\r\n" );
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document.write( ".40x + .90(40) = .50(x+40)\r\n" );
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document.write( "Can you solve that for x? If not post again.\r\n" );
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document.write( "answer:  x = 160 liters\r\n" );
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document.write( "Edwin

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