document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200422>Question 1200422</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 110 people attend a concert and tickets for adults cost $3.5 while tickets for children cost $3.25 and total receipts for the concert was $370, how many of each went to the concert? </SPAN>\n" );
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document.write( "Answer: <font color=red>50 adults, 60 children</font>\r<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "I'll go over 3 methods to solving this problem.\r<BR>\n" );
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document.write( "Method 1\r<BR>\n" );
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document.write( "Let's say that all 110 people were adults<BR>\n" );
document.write( "110 adults --> 110*3.50 = 385 dollars total\r<BR>\n" );
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document.write( "But the total cost should be $370.<BR>\n" );
document.write( "The gap from 385 to 370 is 385-370 = 15.\r<BR>\n" );
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document.write( "Each time we remove an adult, and add a child, then the net change in revenue is -0.25 (since 3.25-3.50 = -0.25)<BR>\n" );
document.write( "In other words, the revenue goes down by $0.25 aka 25 cents, each time we replace an adult with a child.\r<BR>\n" );
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document.write( "x = number of adults that are replaced with children<BR>\n" );
document.write( "0.25x = net decrease in cost<BR>\n" );
document.write( "0.25x = 15<BR>\n" );
document.write( "x = 15/0.25<BR>\n" );
document.write( "x = 60<BR>\n" );
document.write( "We must remove 60 adults and replace them with 60 children.\r<BR>\n" );
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document.write( "We go from 110 adults to 110-60 = 50 adults.<BR>\n" );
document.write( "We go from 0 children to 0+60 = 60 children.\r<BR>\n" );
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document.write( "Method 2\r<BR>\n" );
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document.write( "a = number of adults<BR>\n" );
document.write( "110-a = number of children\r<BR>\n" );
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document.write( "3.50a = revenue from the adults<BR>\n" );
document.write( "3.25(110-a) = revenue from the children<BR>\n" );
document.write( "3.50a+3.25(110-a) = total revenue\r<BR>\n" );
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document.write( "3.50a+3.25(110-a) = 370<BR>\n" );
document.write( "3.50a+357.5-3.25a = 370<BR>\n" );
document.write( "0.25a+357.5 = 370<BR>\n" );
document.write( "0.25a = 370-357.5<BR>\n" );
document.write( "0.25a = 12.5<BR>\n" );
document.write( "a = 12.5/0.25<BR>\n" );
document.write( "a = 50<BR>\n" );
document.write( "110-a = 110-50 = 60\r<BR>\n" );
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document.write( "Method 3\r<BR>\n" );
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document.write( "x = number of adults<BR>\n" );
document.write( "y = number of children\r<BR>\n" );
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document.write( "x+y = 110 total people<BR>\n" );
document.write( "3.50x+3.25y = 375 total revenue\r<BR>\n" );
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document.write( "Use a graphing app like Desmos to plot each of those equations. <BR>\n" );
document.write( "The two lines intersect at (x,y) = (50,60) to indicate x = 50 adults and y = 60 children.\r<BR>\n" );
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document.write( "Here's the link to the interactive graph<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.desmos.com/calculator/zmecbj4vep\">https://www.desmos.com/calculator/zmecbj4vep</a>\r<BR>\n" );
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document.write( "Feel free to explore other methods to solving this type of problem.\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "1 adult = $3.50<BR>\n" );
document.write( "50 adults = 50*$3.50 = $175<BR>\n" );
document.write( "1 child = $3.25<BR>\n" );
document.write( "60 children = 60*$3.25 = $195<BR>\n" );
document.write( "50 adults + 60 children = 110 people total<BR>\n" );
document.write( "50 adults + 60 children = $175 + $195 = $370<BR>\n" );
document.write( "The answers are fully verified.<BR>\n" );
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