document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=346645>Question 346645</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write a system of two equations using x and y to represent the following problem. A chemist is mixing two solutions together. <BR>\n" );
document.write( "The chemist wants 100 gallons when complete. He is mixing a 24% solution with a 50% solution to get a 36% solution. How many gallons of each will he use?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #247850 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=247850\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write a system of two equations using x and y to represent the following problem. A chemist is mixing two solutions together. <BR>\n" );
document.write( "The chemist wants 100 gallons when complete. He is mixing a 24% solution with a 50% solution to get a 36% solution. How many gallons of each will he use?<BR>\n" );
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document.write( "Let x = amount of 24% solution<BR>\n" );
document.write( "and y = amount of 50% solution<BR>\n" );
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document.write( "From: \"The chemist wants 100 gallons when complete.\" we get equation 1:<BR>\n" );
document.write( "x+y = 100<BR>\n" );
document.write( "From: \"He is mixing a 24% solution with a 50% solution to get a 36% solution.\" we get equation 2:<BR>\n" );
document.write( ".24x + .50y = .36(100)<BR>\n" );
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document.write( "Solve equation 1 for y:<BR>\n" );
document.write( "x+y = 100<BR>\n" );
document.write( "y = 100-x<BR>\n" );
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document.write( "Substitute the above into equation 2:<BR>\n" );
document.write( ".24x + .50y = .36(100)<BR>\n" );
document.write( ".24x + .50(100-x) = .36(100)<BR>\n" );
document.write( ".24x + 50-.50x = 36<BR>\n" );
document.write( "50-.26x = 36<BR>\n" );
document.write( "-.26x = -14<BR>\n" );
document.write( "x = 53.85 gallons (of 24% solution)<BR>\n" );
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document.write( "to find 50% solution substitute above into equation 1:<BR>\n" );
document.write( "x+y = 100<BR>\n" );
document.write( "53.85+y = 100<BR>\n" );
document.write( "y = 46.15 gallons\r<BR>\n" );
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