document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=322012>Question 322012</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Angie bought some golf balls for $24. If each ball had cost $0.50 less, she could have purchased one more ball for the same amount of money. How many golf balls did Angie buy? </SPAN>\n" );
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document.write( "Here is another method:\r<BR>\n" );
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document.write( "Let n = number of balls purchased<BR>\n" );
document.write( "Let p = price per ball<BR>\n" );
document.write( "Therefore:<BR>\n" );
document.write( "n * p = 24<BR>\n" );
document.write( "(n + 1)(p - 0.5) = 24<BR>\n" );
document.write( "Therefore:<BR>\n" );
document.write( "p = 24/n<BR>\n" );
document.write( "(n + 1)((24/n) - 0.5) = 24<BR>\n" );
document.write( "24 - 0.5n + (24/n) - 0.5 = 24<BR>\n" );
document.write( "-0.5n + (24/n) - 0.5 = 0<BR>\n" );
document.write( "Multiply through by -2n:<BR>\n" );
document.write( "n^2 + n - 48 = 0<BR>\n" );
document.write( "n = (-1 +/- sqrt(1^2 - 4(1)(-48))) / (2*1)<BR>\n" );
document.write( "n = (-1 +/- sqrt(1 + 192)) / 2<BR>\n" );
document.write( "n = (-1 +/- sqrt(193)) / 2<BR>\n" );
document.write( "n = -0.5 +/- sqrt(48.25)<BR>\n" );
document.write( "n =~ 6.47 or -7.47\r<BR>\n" );
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document.write( "Suppose she bought 6 balls, so they each cost $4. If they had cost $3.50, then $24 would still not be enough to buy 7 balls. So that doesn't work.<BR>\n" );
document.write( "Suppose she bought 7 balls, so they each cost about $3.43. If they had cost $2.93, she could have bought 8 balls for $24 (and received $0.56 in change).<BR>\n" );
document.write( "Suppose she bought 8 balls, so they each cost $3. If they had cost $2.50, she could have bought 9 balls for $24 (and received $1.50 in change).<BR>\n" );
document.write( "Suppose she bought 9 balls, so they each cost about $2.67. If they had cost $2.17, she could have bought at least 11 balls for $24. So that doesn't work.\r<BR>\n" );
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document.write( "So the answer must be 7 (or 8).<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );