document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1132020>Question 1132020</A>: <I><SPAN STYLE=\"word-break: break-all;\"> On weekdays, a movie theater charges different rates for adults and children. If 3 adults and 2 children go for a movie on a weekday, the total cost of the tickets is $31. If 2 adults and 3 children go on a weekday, the total cost of the tickets is $29. If a group of adults and 6 children go to the movie theater on a weekday and pay $58 for tickets, how many adults are in this group? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #748830 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=748830\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let a be the cost of a ticket for an adult and c be the cost for a child<BR>\n" );
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document.write( "1) 3a +2c = 31<BR>\n" );
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document.write( "2) 2a +3c = 29<BR>\n" );
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document.write( "subtract equation 2 from equation 1<BR>\n" );
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document.write( "a -c = 2<BR>\n" );
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document.write( "3) a = c +2<BR>\n" );
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document.write( "substitute for a in equation 1<BR>\n" );
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document.write( "3(c+2) +2c = 31<BR>\n" );
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document.write( "3c +6 +2c = 31<BR>\n" );
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document.write( "5c = 25<BR>\n" );
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document.write( "c = 5<BR>\n" );
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document.write( "substitute for c in equation 3<BR>\n" );
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document.write( "a = 5 +2 = 7<BR>\n" );
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document.write( "let x be the number of adults in the group<BR>\n" );
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document.write( "4) 7x +6(5) = 58<BR>\n" );
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document.write( "7x +30 =58<BR>\n" );
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document.write( "7x = 28<BR>\n" );
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document.write( "x = 4<BR>\n" );
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document.write( "There are 4 adults in the group<BR>\n" );
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document.write( "check this answer with equation 4<BR>\n" );
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document.write( "7(4) +6(5) = 58<BR>\n" );
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document.write( "28 +30 = 58<BR>\n" );
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document.write( "58 = 58<BR>\n" );
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document.write( "answer checks<BR>\n" );
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document.write( "Note the cost of an adult ticket is $7 and a child ticket is $5<BR>\n" );
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document.write( "Check these cost values<BR>\n" );
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document.write( "equation 1<BR>\n" );
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document.write( "3(7) +2(5) = 31<BR>\n" );
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document.write( "21 +10 = 31<BR>\n" );
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document.write( "31 = 31<BR>\n" );
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document.write( "equation 2<BR>\n" );
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document.write( "2(7) +3(5) = 29<BR>\n" );
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document.write( "14 +15 = 29 <BR>\n" );
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document.write( "29 = 29<BR>\n" );
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document.write( "answers check<BR>\n" );
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document.write( ": </SPAN>\n" );
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