document.write( "Question 73828: A total of 434 people attended a community theatre performance. The admission prices were $9.00 for adults, $7.50 for students, and $8.00 for senior citizens. The ticket sales totaled $3712. At the theatre's next board meeting, the finance manager proposed that for the next play they raise prices to $11.00 for adults, $8.50 for students, and $8.50 for senior citizens. He said that if the exact same number of people attend the next performance, the ticket sales would be $4374. How many adults, students, and senior citizens attended the play? \n" ); document.write( "
Algebra.Com's Answer #52889 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
Write an equation for each statement; a=adults, b=kids, c=old folks
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\n" ); document.write( "\"A total of 434 people attended a community theatre performance.\"
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\n" ); document.write( "eq1: a + b + c = 434
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\n" ); document.write( "\"The admission prices were $9.00 for adults, $7.50 for students, and $8.00 for senior citizens. The ticket sales totaled $3712.\"
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\n" ); document.write( "eq2: 9a + 7.5b + 8c = 3712
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\n" ); document.write( "\"At the theatre's next board meeting, the finance manager proposed that for the next play they raise prices to $11.00 for adults, $8.50 for students, and $8.50 for senior citizens. Ticket sales would be 4374\"
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\n" ); document.write( "eq3: 11a + 8.5b + 8.5c = 4374
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\n" ); document.write( "He said that if the exact same number of people attend the next performance, the ticket sales would be $4374. How many adults, students, and senior citizens attended the play?
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\n" ); document.write( "A matrix could be used it would be:
\n" ); document.write( "1 + 1 + 1 + 434
\n" ); document.write( "9 + 7.5 + 8 + 3712
\n" ); document.write( "11 + 8.5 + 8.5 + 4374
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\n" ); document.write( "However elimination can also be used, here is that method.
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\n" ); document.write( "Subtract eq 2 from eq 3
\n" ); document.write( "Then subtract eq 1 from that result:
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\n" ); document.write( "11a + 8.5b + 8.5c =4374
\n" ); document.write( " 9a + 7.5b + 8c = 3712
\n" ); document.write( "------------------------ subtract:
\n" ); document.write( "2a + 1b + .5c = 662
\n" ); document.write( "1a + 1b + 1c = 434
\n" ); document.write( "---------------------- subtracting eliminates b:
\n" ); document.write( "1a + 0b - .5c = 228
\n" ); document.write( "a - .5c = 228; a two unknown equation
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\n" ); document.write( "Multiply equation 1 by 7.5 and subtract it from equation 2:
\n" ); document.write( " 9a + 7.5b + 8c = 3712
\n" ); document.write( "7.5a + 7.5b + 7.5c = 3255
\n" ); document.write( "---------------------------subtracting eliminates b again:
\n" ); document.write( "1.5a + 0b + .5c = 457
\n" ); document.write( "1.5a + .5c = 457; another two unknown equation
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\n" ); document.write( "Add our \"two unknown\" equations and find a:
\n" ); document.write( "a - .5c = 228
\n" ); document.write( "1.5a + .5c = 457
\n" ); document.write( "---------------------adding eliminates c
\n" ); document.write( "2.5a + 0c = 685
\n" ); document.write( "a = 685/2.5
\n" ); document.write( "a = 274 adults
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\n" ); document.write( "Use a - .5c = 228 to find c, substitute 274 for a
\n" ); document.write( "274 - .5c = 228
\n" ); document.write( "-.5c = 228 - 274
\n" ); document.write( "-.5c = -46
\n" ); document.write( "c =-46/-.5
\n" ); document.write( "c = +92 old folks
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\n" ); document.write( "I'm sure you can find the number of kids, equation 1 will work well:
\n" ); document.write( " Check the solutions in eq 2 or 3.
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