document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191509>Question 1191509</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A group of office workers had some prize money to distribute among themselves. When all but one took $9 each, the last person only received $5. When they all took $8 each, there was $12 left over. How much had they won? </SPAN>\n" );
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document.write( "P = total prize money in dollars<BR>\n" );
document.write( "n = number of people<BR>\n" );
document.write( "n-1 = all but one person\r<BR>\n" );
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document.write( "All but one took $9 each, so we have (n-1)*9 = 9n-9 dollars taken. <BR>\n" );
document.write( "The amount of money left over is P-(9n-9) = P-9n+9 which is set equal to the stated $5\r<BR>\n" );
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document.write( "P-9n+9 = 5<BR>\n" );
document.write( "P = 5+9n-9<BR>\n" );
document.write( "P = 9n-4\r<BR>\n" );
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document.write( "In the second scenario, all n workers took $8 each. <BR>\n" );
document.write( "They took a total of 8n dollars. <BR>\n" );
document.write( "There is $12 left over, so,<BR>\n" );
document.write( "P - 8n = 12\r<BR>\n" );
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document.write( "Now apply substitution<BR>\n" );
document.write( "P - 8n = 12<BR>\n" );
document.write( "9n-4 - 8n = 12<BR>\n" );
document.write( "n-4 = 12<BR>\n" );
document.write( "n = 12+4<BR>\n" );
document.write( "n = 16<BR>\n" );
document.write( "There are 16 office workers total.<BR>\n" );
document.write( "If all but one (aka 15 people) take $9 each, then we have 15*9 = 135 dollars taken. Add on the leftover $5 to get to 135+5 = <font color=red>$140</font>\r<BR>\n" );
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document.write( "Or you can compute P like this<BR>\n" );
document.write( "P = 9n-4<BR>\n" );
document.write( "P = 9*16-4<BR>\n" );
document.write( "P = 144 - 4<BR>\n" );
document.write( "P = <font color=red>140</font>\r<BR>\n" );
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document.write( "Yet another way is to do<BR>\n" );
document.write( "P - 8n = 12<BR>\n" );
document.write( "P = 8n+12<BR>\n" );
document.write( "P = 8*16+12<BR>\n" );
document.write( "P = 128+12<BR>\n" );
document.write( "P = <font color=red>140</font><BR>\n" );
document.write( "Like with many topics in math, there are multiple routes to take. <BR>\n" );
document.write( "Feel free to use your favorite.\r<BR>\n" );
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document.write( "Answer: <font color=red>140 dollars</font><BR>\n" );
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document.write( " </SPAN>\n" );
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