document.write( "Question 1165000: Three girls, Ann, Betty and Cynthia, each have a younger brother, Dylan,
\n" ); document.write( "Ernie and Frank, respectively. All six children do some fruit picking for
\n" ); document.write( "the local farmer. The farmer agrees to pay each child as many dollars per
\n" ); document.write( "basket as the number of baskets of fruit collected by that child. Each of
\n" ); document.write( "the girls earned $45 more than her brother, and all six children collected
\n" ); document.write( "a different number of baskets. How much did the farmer pay them all in
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Algebra.Com's Answer #789447 by ikleyn(52943) $\"\"$ $\"About$

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\n" ); document.write( "Three girls, Ann, Betty and Cynthia, each have a younger brother, Dylan,
\n" ); document.write( "Ernie and Frank, respectively. All six children do some fruit picking for
\n" ); document.write( "the local farmer. The farmer agrees to pay each child as many dollars per
\n" ); document.write( "basket as the number of baskets of fruit collected by that child. Each of
\n" ); document.write( "the girls earned $45 more than her brother, and all six children collected
\n" ); document.write( "a different number of baskets. How much did the farmer pay them all in total ?
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document.write( "Let x be the number of baskets collected by some girl, and y be the number of basket collected by her brother.\r\n" );
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document.write( "Then for each such a pair, we have this equation\r\n" );
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document.write( "    x^2 - y^2 = 45.\r\n" );
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document.write( "Factor left side to get\r\n" );
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document.write( "    (x-y)*(x+y) = 45.\r\n" );
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document.write( "45 has these decompositions in the product of factors  1*45,  3*15  and  9*5.\r\n" );
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document.write( "These decompositions produce these systems of equations\r\n" );
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document.write( "a)  x - y =  1\r\n" );
document.write( "    x + y = 45\r\n" );
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document.write( "        with the solution  x = 23, y = 22;\r\n" );
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document.write( "b)  x - y =  3\r\n" );
document.write( "    x + y = 15\r\n" );
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document.write( "        with the solution  x = 9, y = 6;\r\n" );
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document.write( "c)  x - y =  5\r\n" );
document.write( "    x + y =  9\r\n" );
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document.write( "        with the solution  x = 7, y = 2.\r\n" );
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document.write( "These are all possible solutions to the numbers of baskets collected by the children.\r\n" );
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document.write( "There is NO other solutions.\r\n" );
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document.write( "Hence, the total pay was   = 1183 dollars.    ANSWER\r\n" );
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