document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202435>Question 1202435</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The admission fees at an amusement park are $4.25 for children and $6.00 for adults. On a certain day, 282 people entered the park, and the admission fees collected totaled $1,391.00. How many children and how many adults attended the amusement park that day?\r<BR>\n" );
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document.write( "There were children and adults that attended the amusement park that day. </SPAN>\n" );
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document.write( "If all 282 people were adults, then the total admission fees collected would be 6*282 = 1692 dollars.\r<BR>\n" );
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document.write( "This amount is too large compared to $1391. The gap is 1692-1391 = 301 dollars.\r<BR>\n" );
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document.write( "Let's replace some adults with children.<BR>\n" );
document.write( "For each adult replaced with a child, the net amount collected goes down by 6-4.25 = 1.75 dollars per person.\r<BR>\n" );
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document.write( "Doing this x number of times means the total amount goes down by 1.75x dollars.<BR>\n" );
document.write( "We want this decrease to go down by the gap 301 found earlier.<BR>\n" );
document.write( "1.75x = 301<BR>\n" );
document.write( "x = 301/1.75<BR>\n" );
document.write( "x = 172<BR>\n" );
document.write( "We must remove 172 adults and replace them with 172 children.\r<BR>\n" );
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document.write( "282 adults drops down to 282 - 172 = 110 adults<BR>\n" );
document.write( "0 children increases to 0+172 = 172 children\r<BR>\n" );
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document.write( "An alternative is to solve this system of equations<BR>\n" );
document.write( "c+a = 282<BR>\n" );
document.write( "4.25c+6a = 1391<BR>\n" );
document.write( "where,<BR>\n" );
document.write( "c = number of children<BR>\n" );
document.write( "a = number of adults\r<BR>\n" );
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document.write( "c+a = 282 solves to c = 282-a<BR>\n" );
document.write( "That is then substituted into the other equation to get 4.25(282-a)+6a = 1391<BR>\n" );
document.write( "I'll skip the steps but you should get a = 110 and it leads to c = 172.\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "172 children + 110 adults = 282 people total\r<BR>\n" );
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document.write( "P = revenue from the children<BR>\n" );
document.write( "P = 172*4.25 = 731 dollars<BR>\n" );
document.write( "Q = revenue from the adults<BR>\n" );
document.write( "Q = 110*6 = 660 dollars<BR>\n" );
document.write( "P+Q = total revenue<BR>\n" );
document.write( "P+Q = 731+660<BR>\n" );
document.write( "P+Q = 1391 dollars total revenue<BR>\n" );
document.write( "We have confirmed the solutions.\r<BR>\n" );
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document.write( "Answer:<BR>\n" );
document.write( "172 children<BR>\n" );
document.write( "110 adults<BR>\n" );
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