document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=151442>Question 151442</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm having some trouble solving these problems please help me.\r<BR>\n" );
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document.write( "Use algebraic techniques to solve rate problems and percent problems:\r<BR>\n" );
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document.write( "1.) Five tables and eight chairs cost $115; three tables and five chairs cost $70. Determine the cost of each table and each chair?\r<BR>\n" );
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document.write( "2.)A merchant sold his entire stock of shirts and ties for $1000, the shirts being priced at 3 for $10 and the ties at $2 each. If he sold 1/2 of the shirts and 2/3 of the ties he would have collected $600. How many of each kind did he sell?\r<BR>\n" );
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document.write( "3.)Determine the speed of a motorboat in still water and the speed of the river current, if it takes 3 hr to travel a distance of 45 mi upstream and 2 hr to travel 50 mi downstream?\r<BR>\n" );
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document.write( "Please and thank  you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #111332 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=111332\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.) Five tables and eight chairs cost $115; three tables and five chairs cost $70. Determine the cost of each table and each chair?<BR>\n" );
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document.write( "Let x = cost of tables; let y = cost of chairs<BR>\n" );
document.write( "Write an equation for each statement:<BR>\n" );
document.write( "\"Five tables and eight chairs cost $115;\"<BR>\n" );
document.write( "5x + 8y = 115<BR>\n" );
document.write( "\"three tables and five chairs cost $70.\"<BR>\n" );
document.write( "3x + 5y = 70<BR>\n" );
document.write( "Use elimination here, Multiply the 1st equation by 3, the 2nd equation by 5<BR>\n" );
document.write( "15x + 25y = 350<BR>\n" );
document.write( "15x + 24y = 345<BR>\n" );
document.write( "-------------------subtraction eliminates x, find y<BR>\n" );
document.write( "0x + 1y = 5<BR>\n" );
document.write( "y = $5 is cost of one chair<BR>\n" );
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document.write( "Find x using the 1st equation:<BR>\n" );
document.write( "5x + 8(5) = 115<BR>\n" );
document.write( "5x + 40 = 115<BR>\n" );
document.write( "5x = 115 - 40<BR>\n" );
document.write( "5x = 75<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75%2F5 ALIGN=MIDDLE  ALT=\"75%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = $15 is cost of one table<BR>\n" );
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document.write( "Check solutions in 2nd equation<BR>\n" );
document.write( "3(15) + 5(5) = <BR>\n" );
document.write( "45 + 25 = 70<BR>\n" );
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document.write( "2.)A merchant sold his entire stock of shirts and ties for $1000, the shirts being priced at 3 for $10 and the ties at $2 each. If he sold 1/2 of the shirts and 2/3 of the ties he would have collected $600. How many of each kind did he sell?<BR>\n" );
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document.write( "Let x = no. of shirts sold<BR>\n" );
document.write( "let y = no. of ties<BR>\n" );
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document.write( "Write an equation for each statement:<BR>\n" );
document.write( "\"A merchant sold his entire stock of shirts and ties for $1000, the shirts being priced at 3 for $10 and the ties at $2 each\"<BR>\n" );
document.write( "10(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F3 ALIGN=MIDDLE  ALT=\"x%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >) + 2y = 1000<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810x%29%2F3 ALIGN=MIDDLE  ALT=\"%2810x%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 2y = 1000<BR>\n" );
document.write( "multiply equation by 3 to get rid of the denominator<BR>\n" );
document.write( "10x + 6y = 3000; (1st equation)<BR>\n" );
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document.write( "\"If he had sold only 1/2 of the shirts and 2/3 of the ties he would have collected $600. How many of each kind did he sell?\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810x%29%2F3 ALIGN=MIDDLE  ALT=\"%2810x%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >*2y = 600<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810x%29%2F6 ALIGN=MIDDLE  ALT=\"%2810x%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284y%29%2F3 ALIGN=MIDDLE  ALT=\"%284y%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 600<BR>\n" );
document.write( "Reduce fraction<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%29%2F3 ALIGN=MIDDLE  ALT=\"%285x%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284y%29%2F3 ALIGN=MIDDLE  ALT=\"%284y%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 600<BR>\n" );
document.write( "Multiply equation by 3 to get rid of the denominator<BR>\n" );
document.write( "5x + 4y = 1800<BR>\n" );
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document.write( "multiply above equation by 2 and subtract the 1st equation:<BR>\n" );
document.write( "10x + 8y = 3600<BR>\n" );
document.write( "10x + 6y = 3000<BR>\n" );
document.write( "-----------------subtraction eliminates x<BR>\n" );
document.write( "0x + 2y = 600<BR>\n" );
document.write( "y = 300 ties sold<BR>\n" );
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document.write( "Find x, use eq: 10x + 6y = 3000<BR>\n" );
document.write( "10x + 6(300) = 3000<BR>\n" );
document.write( "10x + 1800 = 3000<BR>\n" );
document.write( "10x = 3000 - 1800<BR>\n" );
document.write( "10x = 3000 - 1800<BR>\n" );
document.write( "10x = 1200<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1200%2F10 ALIGN=MIDDLE  ALT=\"1200%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 120 shirts sold<BR>\n" );
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document.write( "Check solution in <BR>\n" );
document.write( "5x + 4y = 1800<BR>\n" );
document.write( "5(120) + 4(300) = <BR>\n" );
document.write( "600 + 1200 = 1800<BR>\n" );
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document.write( "3.)Determine the speed of a motorboat in still water and the speed of the river current, if it takes 3 hr to travel a distance of 45 mi upstream and 2 hr to travel 50 mi downstream?<BR>\n" );
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document.write( "Let x = speed of boat in still water<BR>\n" );
document.write( "Let y = speed of the current<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(x+y) = speed with the current<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(x-y) = speed against the current<BR>\n" );
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document.write( "Write a distance equation for each trip: Dist = time * speed<BR>\n" );
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document.write( "2(x + y) = 50<BR>\n" );
document.write( "3(x - y) = 45<BR>\n" );
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document.write( "Simplify divide the 1st equation by 2 and the 2nd equation by 3; results:<BR>\n" );
document.write( "x + y = 25<BR>\n" );
document.write( "x - y = 15<BR>\n" );
document.write( "------------addition eliminates y, find x<BR>\n" );
document.write( "2x = 40<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2F2 ALIGN=MIDDLE  ALT=\"40%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 20 mph speed of boat in still water<BR>\n" );
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document.write( "Find y using; x + y = 25<BR>\n" );
document.write( "20 + y = 25<BR>\n" );
document.write( "y = 25 - 20<BR>\n" );
document.write( "y = 5 mph speed of the river<BR>\n" );
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document.write( "Check solutions in the 2nd original equation<BR>\n" );
document.write( "3(x - y) = 45<BR>\n" );
document.write( "3(20-5) = 45<BR>\n" );
document.write( "3(15) = 45; confirms our solution  </SPAN>\n" );
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