document.write( "Question 424758: I really don't understand word problems, would you please help me with this problem?\r
\n" ); document.write( "\n" ); document.write( "A researcher orders a broth of 8% glucose for her lab. However, she needs a stronger broth,one that is 14.1% glucose. Fortunately, she has 70.6 liters of 41% glucose broth in the stock room. How much 14.1% glucose can she make? \n" ); document.write( "

Algebra.Com's Answer #296041 by AnlytcPhil(1806) $\"\"$ $\"About$

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A researcher orders a broth of 8% glucose for her lab. However, she needs a stronger broth,one that is 14.1% glucose. Fortunately, she has 70.6 liters of 41% glucose broth in the stock room. How much 14.1% glucose can she make?
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document.write( "What she has are two containers each containing some glucose\r\n" );
document.write( "mixed with water, One is too strong and the other is too weak,\r\n" );
document.write( "so she wants to add enough of the weak to all of the strong \r\n" );
document.write( "to dilute it down to the medium strength that she wants.\r\n" );
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document.write( "Let the amount of the weak that she needs to add to the strong \r\n" );
document.write( "be x liters.\r\n" );
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document.write( "We make this chart:\r\n" );
document.write( "      \r\n" );
document.write( "         liters of liquid | strength | liters of pure glucose in the liquid \r\n" );
document.write( "---------------------------------------------------------------------------\r\n" );
document.write( "strong                    |          |\r\n" );
document.write( "weak                      |          |          \r\n" );
document.write( "medium                    |          |\r\n" );
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document.write( "We have 70.6 liters of liquid of the strong and we add x liters of\r\n" );
document.write( "liquid of the weak so we will end up with (70.6 + x) liters of the\r\n" );
document.write( "medium strength we want.\r\n" );
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document.write( "So we fill in the first column, which is the number of liters of liquid\r\n" );
document.write( "of the strong and of the weak, and the final amout of liquid of medium\r\n" );
document.write( "strength that we want to end up with.  We also fill in the middle\r\n" );
document.write( "column with the three strengths.   \r\n" );
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document.write( "         liters of liquid | strength | liters of pure glucose in the liquid\r\n" );
document.write( "---------------------------------------------------------------------------\r\n" );
document.write( "strong           70.6     |    41%   |           \r\n" );
document.write( "weak               x      |     8%   |             \r\n" );
document.write( "medium         70.6 + x   |   14.1%  |         \r\n" );
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document.write( "Then we fill in the liters of pure glucose contained in each \r\n" );
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document.write( "         liters of liquid | strength | liters of pure glucose in the liquid\r\n" );
document.write( "---------------------------------------------------------------------------\r\n" );
document.write( "strong           70.6     |    41%   |            .41(70.6)  \r\n" );
document.write( "weak               x      |     8%   |             .08x  \r\n" );
document.write( "medium         70.6 + x   |   14.1%  |         .141(70.6 + x)\r\n" );
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document.write( "Liters of pure        Liters of pure       Liters of pure\r\n" );
document.write( "glucose in the    +   glucose in the   =   glucose in the   \r\n" );
document.write( "   strong                 weak                 medium\r\n" );
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document.write( "              .41(70.6) + .08x = .141(70.6 + x)\r\n" );
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document.write( "Solve that and get x = 53.8527541 liters of weak that she needs to \r\n" );
document.write( "add to the strong solution to dilute it down to the medium strength she\r\n" );
document.write( "wants.                  \r\n" );
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document.write( "Edwin

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