document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=731005>Question 731005</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1) A haircut for men costs $15, a haircut for women costs $20, and a haircut for children costs $12.  On a certain day, 70 people spent $1190 on haircuts.  Four more women received haircuts than men and children combined.  How many men, women, and children received haircuts?  For full credit, set up and solve a linear system.  Clearly label any variables you introduce.  Write your answer as a sentence.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #446959 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=446959\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) A haircut for men costs $15, a haircut for women costs $20, and a haircut for children costs $12.  On a certain day, 70 people spent $1190 on haircuts.  Four more women received haircuts than men and children combined.  How many men, women, and children received haircuts?  For full credit, set up and solve a linear system.  Clearly label any variables you introduce.  Write your answer as a sentence.)\r<BR>\n" );
document.write( "\n" );
document.write( "number of men ----------x-------------$15<BR>\n" );
document.write( "number of women ----------y-----------$20<BR>\n" );
document.write( "number of children -------z------------$12\r<BR>\n" );
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document.write( "Number of women= (x+z)+4<BR>\n" );
document.write( "y= x+z+4\r<BR>\n" );
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document.write( "x+y+z=70<BR>\n" );
document.write( "x+x+z+4 +z=70<BR>\n" );
document.write( "2x+2z=66<BR>\n" );
document.write( "/2<BR>\n" );
document.write( "x+z=33......................(1)\r<BR>\n" );
document.write( "\n" );
document.write( "15x+20(x+z+4)+12z=1192\r<BR>\n" );
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document.write( "15x+20x+20z+80+12z=1190\r<BR>\n" );
document.write( "\n" );
document.write( "35x+32z=1110\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "1.00	x	+	1.00	z	=	33.00	.............1	<BR>\n" );
document.write( "Total value								<BR>\n" );
document.write( "35.00	x	+	32.00	z	=	1110.00	.............2	<BR>\n" );
document.write( "Eliminate	y							<BR>\n" );
document.write( "multiply (1)by		-32.00						<BR>\n" );
document.write( "Multiply (2) by		1.00						<BR>\n" );
document.write( "-32.00	x		-32.00	z	=	-1056.00		<BR>\n" );
document.write( "35.00	x	+	32.00	z	=	1110.00		<BR>\n" );
document.write( "Add the two equations								<BR>\n" );
document.write( "3.00	x				=	54.00		<BR>\n" );
document.write( "/	3.00							<BR>\n" );
document.write( "x	=	18.00						<BR>\n" );
document.write( "plug value of			x	in (1)				<BR>\n" );
document.write( "1.00	x	+	1.00	z	=	33.00		<BR>\n" );
document.write( "18.00		+		z	=	33.00		<BR>\n" );
document.write( "				z	=	33.00		-18.00<BR>\n" );
document.write( "				z	=	15.00		<BR>\n" );
document.write( "				z	=	15.00		<BR>\n" );
document.write( "x=	18		number of  	adults			<BR>\n" );
document.write( "z=	15		number of 	children<BR>\n" );
document.write( "y=      37              number of women\r<BR>\n" );
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document.write( "CHECK\r<BR>\n" );
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document.write( "18*15+37*20+15*12=	1190			<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );