document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=182960>Question 182960</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It costs $1.70 to buy supplies to make a fork and $1.30 to buy supplies to make a spoon. The store sells the fork for $5.60 and the spoon for $5.40. They spent $37.90 on materials for forks and spoons. They sold the finished product for $147.20. How many forks and how many spoons did they make?\r<BR>\n" );
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document.write( "I did 1.70x + 1.30y = 37.90 as one of my equations\r<BR>\n" );
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document.write( "5.60x + 5.40y = 147.20 for my other\r<BR>\n" );
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document.write( "I have tried substitution and get tangled up with the decimals<BR>\n" );
document.write( "I have tried addition and get messed up. Seems I get decimal answers and can't seem to work it into a whole fork or whole spoon without it being a decimal. What am I doing wrong, or are my equations not correct and this is where Im going wrong.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #137355 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=137355\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can solve this system with the decimal values, but I always find it easier to get rid of the decimal numbers. To do this, simply multiply both sides of the equations by 100 (which will move EVERY decimal place 2 spots to the right)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.70x+%2B+1.30y+=+37.90 ALIGN=MIDDLE  ALT=\"1.70x+%2B+1.30y+=+37.90\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%281.70x%2B1.30y%29=100%2837.90%29 ALIGN=MIDDLE  ALT=\"100%281.70x%2B1.30y%29=100%2837.90%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 100 to clear out the decimals.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=170x%2B130y=3790 ALIGN=MIDDLE  ALT=\"170x%2B130y=3790\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
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document.write( "So the new first equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=170x%2B130y=3790 ALIGN=MIDDLE  ALT=\"170x%2B130y=3790\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.60x+%2B+5.40y+=+147.20 ALIGN=MIDDLE  ALT=\"5.60x+%2B+5.40y+=+147.20\"   DISABLED_style= \"max-width:90%; height:auto;\" > Move onto the second equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%285.60x%2B5.40y%29=100%28147.20%29 ALIGN=MIDDLE  ALT=\"100%285.60x%2B5.40y%29=100%28147.20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 100 to clear out the decimals.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=560x%2B540y=14720 ALIGN=MIDDLE  ALT=\"560x%2B540y=14720\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
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document.write( "So the new second equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=560x%2B540y=14720 ALIGN=MIDDLE  ALT=\"560x%2B540y=14720\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we have the system of equations:\r<BR>\n" );
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document.write( "Let's use substitution to solve this system.\r<BR>\n" );
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document.write( "Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.\r<BR>\n" );
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document.write( "So let's isolate y in the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=130y=3790-170x ALIGN=MIDDLE  ALT=\"130y=3790-170x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=170x ALIGN=MIDDLE  ALT=\"170x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=130y=-170x%2B3790 ALIGN=MIDDLE  ALT=\"130y=-170x%2B3790\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-170x%2B3790%29%2F%28130%29 ALIGN=MIDDLE  ALT=\"y=%28-170x%2B3790%29%2F%28130%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=130 ALIGN=MIDDLE  ALT=\"130\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28%28-170%29%2F%28130%29%29x%2B%283790%29%2F%28130%29 ALIGN=MIDDLE  ALT=\"y=%28%28-170%29%2F%28130%29%29x%2B%283790%29%2F%28130%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-17%2F13%29x%2B379%2F13 ALIGN=MIDDLE  ALT=\"y=%28-17%2F13%29x%2B379%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-17%2F13%29x%2B379%2F13 ALIGN=MIDDLE  ALT=\"y=%28-17%2F13%29x%2B379%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can now replace each <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the second equation with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-17%2F13%29x%2B379%2F13 ALIGN=MIDDLE  ALT=\"%28-17%2F13%29x%2B379%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" > to solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=560x%2B540highlight%28%28%28-17%2F13%29x%2B379%2F13%29%29=14720 ALIGN=MIDDLE  ALT=\"560x%2B540highlight%28%28%28-17%2F13%29x%2B379%2F13%29%29=14720\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-17%2F13%29x%2B379%2F13 ALIGN=MIDDLE  ALT=\"y=%28-17%2F13%29x%2B379%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the second equation. In other words, replace each <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-17%2F13%29x%2B379%2F13 ALIGN=MIDDLE  ALT=\"%28-17%2F13%29x%2B379%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Notice we've eliminated the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > variables. So we now have a simple equation with one unknown.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=560x%2B%28540%29%28-17%2F13%29x%2B%28540%29%28379%2F13%29=14720 ALIGN=MIDDLE  ALT=\"560x%2B%28540%29%28-17%2F13%29x%2B%28540%29%28379%2F13%29=14720\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=540 ALIGN=MIDDLE  ALT=\"540\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-17%2F13%29x%2B379%2F13 ALIGN=MIDDLE  ALT=\"%28-17%2F13%29x%2B379%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=560x-%289180%2F13%29x%2B204660%2F13=14720 ALIGN=MIDDLE  ALT=\"560x-%289180%2F13%29x%2B204660%2F13=14720\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2813%29%28560x%29-cross%2813%29%28%289180%2Fcross%2813%29%29x%29%2Bcross%2813%29%28204660%2Fcross%2813%29%29=%2813%29%2814720%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply EVERY term by the LCD 13. This will eliminate the fractions \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7280x-9180x%2B204660=191360 ALIGN=MIDDLE  ALT=\"7280x-9180x%2B204660=191360\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply and simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1900x%2B204660=191360 ALIGN=MIDDLE  ALT=\"-1900x%2B204660=191360\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1900x=191360-204660 ALIGN=MIDDLE  ALT=\"-1900x=191360-204660\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 204660 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1900x=-13300 ALIGN=MIDDLE  ALT=\"-1900x=-13300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-13300%29%2F%28-1900%29 ALIGN=MIDDLE  ALT=\"x=%28-13300%29%2F%28-1900%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -1900 to isolate x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "-----------------First Answer------------------------------\r<BR>\n" );
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document.write( "So the first part of our answer is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can plug it into the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-17%2F13%29x%2B379%2F13 ALIGN=MIDDLE  ALT=\"y=%28-17%2F13%29x%2B379%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" > (remember we previously solved for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the first equation).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-17%2F13%29x%2B379%2F13 ALIGN=MIDDLE  ALT=\"y=%28-17%2F13%29x%2B379%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the equation where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > was previously isolated.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-17%2F13%29%287%29%2B379%2F13 ALIGN=MIDDLE  ALT=\"y=%28-17%2F13%29%287%29%2B379%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-119%2F13%2B379%2F13 ALIGN=MIDDLE  ALT=\"y=-119%2F13%2B379%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=20 ALIGN=MIDDLE  ALT=\"y=20\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms and reduce.  \r<BR>\n" );
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document.write( "-----------------Second Answer------------------------------\r<BR>\n" );
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document.write( "So the second part of our answer is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=20 ALIGN=MIDDLE  ALT=\"y=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-----------------Summary------------------------------\r<BR>\n" );
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document.write( "So our answers are:\r<BR>\n" );
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document.write( "So this means that they made 7 forks and 20 spoons\r<BR>\n" );
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