document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203890>Question 1203890</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 68 people attend a concert and tickets for adults cost $3.75 while tickets for children cost $2 and total receipts for the concert was $195.5, how many of each went to the concert? </SPAN>\n" );
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document.write( "Answers: <font color=red>34 adults, 34 children</font>\r<BR>\n" );
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document.write( "Explanation\r<BR>\n" );
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document.write( "Consider the hypothetical scenario that all 68 people are adults.\r<BR>\n" );
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document.write( "If so, then 68*3.75 = 255 dollars would be the revenue. <BR>\n" );
document.write( "However, the actual money pulled in was $195.50\r<BR>\n" );
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document.write( "The gap is 255-195.50 = 59.50<BR>\n" );
document.write( "We must reduce the revenue by $59.50 to arrive at the correct revenue.\r<BR>\n" );
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document.write( "Each time we replace an adult with a child, the net revenue will go down by $1.75 because 3.75 - 2 = 1.75\r<BR>\n" );
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document.write( "n = number of times an adult is replaced by a child<BR>\n" );
document.write( "1.75n = decrease in revenue<BR>\n" );
document.write( "1.75n = 59.50<BR>\n" );
document.write( "n = 59.50/1.75<BR>\n" );
document.write( "n = 34\r<BR>\n" );
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document.write( "If all 68 people were adults, then we must replace 34 of them with children, so that the revenue drops by $59.50 to arrive at $195.50\r<BR>\n" );
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document.write( "68 adults ---> 68-34 = 34 adults<BR>\n" );
document.write( "0 children ---> 0+34 = 34 children\r<BR>\n" );
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document.write( "There are an equal number of adults and children.\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "34 adults + 34 children = 68 people total<BR>\n" );
document.write( "34 adults --> 34*($3.75) = $127.50<BR>\n" );
document.write( "34 children --> 34*($2) = $68<BR>\n" );
document.write( "total money = 127.50+68 = 195.50 dollars<BR>\n" );
document.write( "The answers have been confirmed.\r<BR>\n" );
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document.write( "Another approach would be to graph the equations<BR>\n" );
document.write( "x+y = 68<BR>\n" );
document.write( "3.75x+2y = 195.50<BR>\n" );
document.write( "to find the point of intersection is (x,y) = (34,34)<BR>\n" );
document.write( "Desmos and GeoGebra are two graphing options I recommend.<BR>\n" );
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