document.write( "Question 1069813: A shop that sells nuts has one mixture that is 30% pecans and
\n" ); document.write( "70% peanuts. A second mixture is 40% pecans and 60% peanuts.
\n" ); document.write( "The manager wants to make a mixture that is 38% pecans. She
\n" ); document.write( "wants to use 25 ounces more of the second mixture than the
\n" ); document.write( "first. How many ounces of each mixture should she use?\r
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Algebra.Com's Answer #684936 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The other tutors are correct, but I'll bet your \r\n" );
document.write( "teacher wants you to make a chart for mixture\r\n" );
document.write( "problems. \r\n" );
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document.write( "So begin by making this chart:\r\n" );
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document.write( "         | ounces |  percent   | ounces of | \r\n" );
document.write( "         |of nuts |(as decimal)|  PECANS  |\r\n" );
document.write( "---------|--------|------------------------|\r\n" );
document.write( " 1st mix |        |            |           |\r\n" );
document.write( " 2nd mix |        |            |           | \r\n" );
document.write( "---------|--------|------------|-----------|\r\n" );
document.write( "final mix|        |            |           |\r\n" );
document.write( "

\n" ); document.write( "She wants to use 25 ounces more of the second mixture
\n" ); document.write( "than the first.
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\r\n" );
document.write( "Let x = the number of ounces of the 1st mix.\r\n" );
document.write( "Then x+25 = the number of ounces of the 2nd mix.\r\n" );
document.write( "Fill those in\r\n" );
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document.write( "         | ounces |  percent   | ounces of | \r\n" );
document.write( "         |of nuts |(as decimal)|  PECANS  |\r\n" );
document.write( "---------|--------|------------------------|\r\n" );
document.write( " 1st mix |   x    |            |           |\r\n" );
document.write( " 2nd mix |  x+25  |            |           | \r\n" );
document.write( "---------|--------|------------|-----------|\r\n" );
document.write( "final mix|        |            |           |\r\n" );
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document.write( "Fill in the three percents expressed as decimals (hundredths)\r\n" );
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document.write( "         | ounces |  percent   | ounces of | \r\n" );
document.write( "         |of nuts |(as decimal)|  PECANS  |\r\n" );
document.write( "---------|--------|------------------------|\r\n" );
document.write( " 1st mix |   x    |    0.30    |           |\r\n" );
document.write( " 2nd mix |  x+25  |    0.40    |           | \r\n" );
document.write( "---------|--------|------------|-----------|\r\n" );
document.write( "final mix|        |    0.38    |           |\r\n" );
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document.write( "Add the number of ounces of 1st and 2nd mixes to get the\r\n" );
document.write( "total number of ounces of final mix.\r\n" );
document.write( " x + x+25 = 2x+25.  So fill that in for the ounces of\r\n" );
document.write( "final mix:\r\n" );
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document.write( "         | ounces |  percent   | ounces of | \r\n" );
document.write( "         |of nuts |(as decimal)|  PECANS  |\r\n" );
document.write( "---------|--------|------------------------|\r\n" );
document.write( " 1st mix |   x    |    0.30    |           |\r\n" );
document.write( " 2nd mix |  x+25  |    0.40    |           | \r\n" );
document.write( "---------|--------|------------|-----------|\r\n" );
document.write( "final mix| 2x+25  |    0.38    |           |\r\n" );
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document.write( "Next we fill in the last column with PECANs \r\n" );
document.write( "by taking the percentages of ounces of each of \r\n" );
document.write( "the three mixes.  So we just multiply the two \r\n" );
document.write( "columns:\r\n" );
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document.write( "         | ounces |  percent   | ounces of | \r\n" );
document.write( "         |of nuts |(as decimal)|  PECANS  |\r\n" );
document.write( "---------|--------|------------------------|\r\n" );
document.write( " 1st mix |   x    |    0.30    |0.30x      |\r\n" );
document.write( " 2nd mix |  x+25  |    0.40    |0.40(x+25) | \r\n" );
document.write( "---------|--------|------------|-----------|\r\n" );
document.write( "final mix| 2x+25  |    0.38    |0.38(2x+25)|           \r\n" );
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document.write( "The equation comes from adding up the ounces of PECANS\r\n" );
document.write( "in 1st and 2nd mixes and setting it equal the the number\r\n" );
document.write( "of ounces of PECANS in the final mix:\r\n" );
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document.write( "0.30x + 0.40(x+25) = 0.38(2x+25)\r\n" );
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document.write( "Clear of decimals by moving them 2 places right:\r\n" );
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document.write( "    30x + 40(x+25) = 38(2x+25)\r\n" );
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document.write( "Solve that and get x = \"25%2F3\" or \"8%261%2F3\" \r\n" );
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document.write( "Since we let x = the number of ounces of the 1st mix,\r\n" );
document.write( "the number of ounces of the 30% mixture is \"8%261%2F3\" \r\n" );
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document.write( "Since then x+25 = the number of ounces of the 2nd mix,\r\n" );
document.write( "the number of ounces of the 40% mixture is \"8%261%2F3%2B25=33%261%2F3\".\r\n" );
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document.write( "Edwin

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