document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=166079>Question 166079</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A vendor at the county fair wishes to spend $312 on his milkshake booth and has a goal of earning $1410. He figures he can make a small shake for $0.45 and a large shake for $0.75. He plans to sell a small shake for $2.25 and a large shake for $3.00. Write and solve a system of equations to determine how many of each size shake he will need to make and sell in order to reach his goal. \r<BR>\n" );
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document.write( "Okay my teacher is a crazy lunatic and thinks i am super smart by giving me a super hard question, and i struggle with math in the first place. I understand that i need to find the x and y varibles but im not sure where to begin. theres the amount of money he needs to make a shake and then the amount that hes going to sell them for. am i correct?.... oh and this isnt in my book. he just makes them up randomly. <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 #122479 by </B><A HREF=/tutors/aboutme.mpl?userid=elima4><B>elima4(15)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=elima4><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=122479\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm sure your teacher is not crazy.:)<BR>\n" );
document.write( "Anyway, I'll try and help;<BR>\n" );
document.write( "First of all we know he spends $312 all together. Now lets break that down. To make small milkshakes it cost .45 for each, and for large it cost .75 for each.<BR>\n" );
document.write( "So the equation would be;<BR>\n" );
document.write( "x = small milkshakes<BR>\n" );
document.write( "y = large milkshakes<BR>\n" );
document.write( ".45x + .75y = 312<BR>\n" );
document.write( "Now the lther equation;<BR>\n" );
document.write( "We know he wants to make $1410 altogether, he charges 2.25 for small and 3.00 for large.<BR>\n" );
document.write( "So the equation;<BR>\n" );
document.write( "2.25x + 3y = 1410<BR>\n" );
document.write( "Now we have our two equations, lets solve them.<BR>\n" );
document.write( ".45x+.75y = 312<BR>\n" );
document.write( "2.25x+3y = 1410<BR>\n" );
document.write( "========================<BR>\n" );
document.write( "let solve the first for y;<BR>\n" );
document.write( ".75y = 1410-.45x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281410%29%2F.75+-+%28.45x%29%2F.75 ALIGN=MIDDLE  ALT=\"y+=+%281410%29%2F.75+-+%28.45x%29%2F.75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y= 416-.6x<BR>\n" );
document.write( "Now plug this into either equation for y to find x;<BR>\n" );
document.write( "2.25x +3(416-.6x)=1410<BR>\n" );
document.write( "2.25x + 1248 - 1.8x=1410<BR>\n" );
document.write( ".45x+1248=1410<BR>\n" );
document.write( ".45x=162<BR>\n" );
document.write( "x=360<BR>\n" );
document.write( "Now we have our x, lets find out y;<BR>\n" );
document.write( ".45(360)+.75y=312<BR>\n" );
document.write( "162 + .75y = 312<BR>\n" );
document.write( ".75y = 150<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+150%2F.75 ALIGN=MIDDLE  ALT=\"y+=+150%2F.75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y=200<BR>\n" );
document.write( "Check<BR>\n" );
document.write( ".45(360) + .75(200)=312<BR>\n" );
document.write( "Hope you understand<BR>\n" );
document.write( ":) </SPAN>\n" );
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