document.write( "Question 41551: Brian paid $50 for 12 of honeydews, coconut and watermelons. The unit price for honeydew, coconut and watermelon respectively is $2, $5, and $9. Suppose that Brian bought at least one fruit for each. How many coconuts did Brian buy?\r
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\n" ); document.write( "\n" ); document.write( "The problem is it keeps cancelling out completely. Where did I mess up or is there a better way? \n" ); document.write( "
Algebra.Com's Answer #26835 by AnlytcPhil(1807)\"\" \"About 
You can put this solution on YOUR website!
Brian paid $50 for 12 of honeydews, coconut and watermelons. \r\n" );
document.write( "The unit price for honeydew, coconut and watermelon \r\n" );
document.write( "respectively is $2, $5, and $9. Suppose that Brian bought at \r\n" );
document.write( "least one fruit for each. How many coconuts did Brian buy?\r\n" );
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document.write( "I set up a system of equations\r\n" );
document.write( "h + c + w = 12\r\n" );
document.write( "2h + 5c + 9w = 50 \r\n" );
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document.write( "The problem is it keeps cancelling out completely. Where did \r\n" );
document.write( "I mess up or is there a better way?\r\n" );
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document.write( "1. Use the first equation to eliminate the h term in the \r\n" );
document.write( "   second equation.\r\n" );
document.write( "2. Then, use the second equation to eliminate the c term in \r\n" );
document.write( "   the first equation.\r\n" );
document.write( "3. Solve for h and c in terms of w\r\n" );
document.write( "4. Use the fact that the variables must represent positive \r\n" );
document.write( "   numbers to define inequalities to find w's domain.\r\n" );
document.write( "5. Try all positive integers for w in w's domain.  \r\n" );
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document.write( "1. Use the first equation to eliminate the h term in the \r\n" );
document.write( "   second equation.\r\n" );
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document.write( "Add -2 times the first equarion to 1 times the second\r\n" );
document.write( "equation, but keep the first equation as is:\r\n" );
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document.write( "-2[ h +  c +  w = 12]\r\n" );
document.write( " 1[2h + 5c + 9w = 50] \r\n" );
document.write( "覧覧覧覧覧覧覧覧覧覧予r\n" );
document.write( "        3c + 7w = 26\r\n" );
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document.write( "So our system is not\r\n" );
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document.write( "    h +  c +  w = 12\r\n" );
document.write( "        3c + 7w = 26\r\n" );
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document.write( "2. Then, use the second equation to eliminate the c \r\n" );
document.write( "term in the first equation, but keep the second \r\n" );
document.write( "equation as is.\r\n" );
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document.write( "    -3[h +  c +  w =  12\r\n" );
document.write( "     1[    3c + 7w =  26\r\n" );
document.write( "   覧覧覧覧覧覧覧覧覧覧予r\n" );
document.write( "     -3h      + 4w = -10 \r\n" );
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document.write( "So now our system is\r\n" );
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document.write( "     -3h      + 4w = -10\r\n" );
document.write( "           3c + 7w =  26\r\n" );
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document.write( "3. Solve for h and c in terms of w\r\n" );
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document.write( "Solving the first for h and the second for c\r\n" );
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document.write( "        h = (10+4w)/3\r\n" );
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document.write( "        c  = (26-7w)/3\r\n" );
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document.write( "4. Use the fact that the variables must represent \r\n" );
document.write( "   positive numbers to find w's domain.\r\n" );
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document.write( "All the variables are positive, so\r\n" );
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document.write( "        w > 0\r\n" );
document.write( "(10+4w)/3 > 0, which solves to give w > -10/4\r\n" );
document.write( "(26-7w)/3 > 0, which solves to give w < 26/7 or 3 5/7\r\n" );
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document.write( "So we have 0 < w < 3 5/7\r\n" );
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document.write( "And since w must be an integer, w can only be 1, 2, or 3\r\n" );
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document.write( "We try w = 1.\r\n" );
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document.write( "        h = (10+4w)/3 = (10+4ｷ1)/3 = 14/3, not an integer\r\n" );
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document.write( "        c = (26-7w)/3 = (26-7ｷ1)/3 = 19/3, not an integer\r\n" );
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document.write( "We try w = 2.\r\n" );
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document.write( "        h = (10+4w)/3 = (10+4ｷ2)/3 = 18/3 = 6, an integer,\r\n" );
document.write( "        which is feasible.\r\n" );
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document.write( "        c = (26-7w)/3 = (26-7ｷ2)/3 = 12/3 = 4, an integer, \r\n" );
document.write( "        which is feasible.\r\n" );
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document.write( "We try w = 3.\r\n" );
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document.write( "        h = (10+4w)/3 = (10+4ｷ3)/3 = 22/3, not an integer\r\n" );
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document.write( "        c = (26-7w)/3 = (26-7ｷ3)/3 = 5/3, not an integer\r\n" );
document.write( "      \r\n" );
document.write( "So the only solution is w = 2, h = 6, c = 4.\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com

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