document.write( "Question 1136616: A student has $500. She buys pencil at $50 each and erasers at $20 each. She gets at least 5 of each and the money spent on pencils is over $100 more that that spend on erasers. Find:
\n" ); document.write( "a. How many ways the money can be spent?
\n" ); document.write( "b. The greatest number of pencils that can be bought.
\n" ); document.write( "c. The greatest number of erasers that can be bought. \n" ); document.write( "
Algebra.Com's Answer #754421 by Edwin McCravy(20055)\"\" \"About 
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A student has $500. She buys pencil at $50 each and erasers at $20 each. '
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document.write( "Very expensive pencils and erasers!!!\r\n" );
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document.write( "Let x = the number of pencils.\r\n" );
document.write( "Let y = the number of erasers. Then:\r\n" );
document.write( "Money spent on pencils = 50x\r\n" );
document.write( "Money spent on erasers = 20y\r\n" );
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document.write( "So \"50x%2B20y%3C=500\" which simplifies to \"5x%2B2y%3C=50\"
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\n" ); document.write( "\n" ); document.write( "She gets at least 5 of each
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document.write( "So \"x%3E=5\" and \"y%3E=5\"

\n" ); document.write( "and the money spent on pencils is over $100 more that that spend on erasers.
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document.write( "So \"50x+%3E+20y+%2B+100\" which simplifies to \"5x%3E2y%2B10\"\r\n" );
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document.write( "The system of inequalities is:\r\n" );
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document.write( "\"system%285x%2B2y%3C=50%2C5x%3E2y%2B10%2Cx%3E=5%2Cy%3E=5%29\"\r\n" );
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document.write( "We graph the 5 lines, the second one dotted, the others solid:\r\n" );
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document.write( "\"system%285x%2B2y=50%2C5x=2y%2B10%2Cx=5%2Cy=5%29\"\r\n" );
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document.write( "The feasible region is the quadrilateral below.  Since the number \r\n" );
document.write( "of pencils and erasers must be whole numbers, we circle all the \r\n" );
document.write( "points with whole numbers for both coordinates (called \"lattice \r\n" );
document.write( "points\").  We include all the lattice points which are on any of\r\n" );
document.write( "the sides of the quadrilateral which are solid, but not on the\r\n" );
document.write( "side which is dotted.  [Note: We cannot include (6,10) because \r\n" );
document.write( "even though it is on a side which is solid, it is also on the \r\n" );
document.write( "side which is dotted.\r\n" );
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\n" ); document.write( "Find:
\n" ); document.write( "a. How many ways the money can be spent?
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document.write( "These are represented by the circled points in or on the \r\n" );
document.write( "feasible region (inside the quadrilateral or on the \r\n" );
document.write( "quadrilateral's solid sides but not on the dotted side):\r\n" );
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document.write( "We count the circled points and find there are 12 of them. \r\n" );
document.write( "(x=no. of pencils, y=no. of erasers):\r\n" );
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document.write( "(5,5), (5,6), (5,7), (6,5), (6,6), (6,7), \r\n" );
document.write( "(6,8), (6,9), (7,5), (7,6), (7,7), (8,5).

\n" ); document.write( "b. The greatest number of pencils that can be bought.
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document.write( "That's the greatest x-coordinate, which is 8.

\n" ); document.write( "c. The greatest number of erasers that can be bought.
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document.write( "That's the greatest y-coordinate, which is 9. \r\n" );
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document.write( "Edwin
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