document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=89688>Question 89688</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A donut shop sells a box of 7 cream-filled and 5 jelly donuts for $6.32, and a box of 4 cream filled and 8 jelly donuts for $6.08.  Find the cost of a single cream filled and a single jelly donut\".\r<BR>\n" );
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document.write( "I know it's 2 variables and 2 equations.  I have it set up like this\r<BR>\n" );
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document.write( "7x + 5y = 6.32<BR>\n" );
document.write( "4x + 8y = 6.08\r<BR>\n" );
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document.write( "I was thinking to get rid of the decimals by mult by 100.  I need some help please and maybe step by step instructions.  Thank you so much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #65148 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=65148\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 7x + 5y = 6.32<BR>\n" );
document.write( "4x + 8y = 6.08 \r<BR>\n" );
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document.write( "Multiply both sides 100\r<BR>\n" );
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document.write( "100(7x + 5y) =100* 6.32<BR>\n" );
document.write( "100(4x + 8y) =100* 6.08 \r<BR>\n" );
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document.write( "Distribute and multiply\r<BR>\n" );
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document.write( "700x+500y=632<BR>\n" );
document.write( "400x+800y=608\r<BR>\n" );
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document.write( "Now lets use elimination to solve for x and y\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solving_linear_system_by_elimination.solver>Solving a System of Linear Equations by Elimination/Addition</A></TD></TR>\n" );
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document.write( "  <BR>\n" );
document.write( "  Lets start with the given system of linear equations<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=700%2Ax%2B500%2Ay=632 ALIGN=MIDDLE  ALT=\"700%2Ax%2B500%2Ay=632\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400%2Ax%2B800%2Ay=608 ALIGN=MIDDLE  ALT=\"400%2Ax%2B800%2Ay=608\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).<BR>\n" );
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document.write( "  So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero.<BR>\n" );
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document.write( "  So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 700 and 400 to some equal number, we could try to get them to the LCM.<BR>\n" );
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document.write( "  Since the LCM of 700 and 400 is 2800, we need to multiply both sides of the top equation by 4 and multiply both sides of the bottom equation by -7 like this:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A%28700%2Ax%2B500%2Ay%29=%28632%29%2A4 ALIGN=MIDDLE  ALT=\"4%2A%28700%2Ax%2B500%2Ay%29=%28632%29%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the top equation (both sides) by 4<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7%2A%28400%2Ax%2B800%2Ay%29=%28608%29%2A-7 ALIGN=MIDDLE  ALT=\"-7%2A%28400%2Ax%2B800%2Ay%29=%28608%29%2A-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the bottom equation (both sides) by -7<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  So after multiplying we get this:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2800%2Ax%2B2000%2Ay=2528 ALIGN=MIDDLE  ALT=\"2800%2Ax%2B2000%2Ay=2528\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2800%2Ax-5600%2Ay=-4256 ALIGN=MIDDLE  ALT=\"-2800%2Ax-5600%2Ay=-4256\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Notice how 2800 and -2800 add to zero (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2800%2B-2800=0 ALIGN=MIDDLE  ALT=\"2800%2B-2800=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "  Now add the equations together. In order to add 2 equations, group like terms and combine them<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282800%2Ax-2800%2Ax%29%2B%282000%2Ay-5600%2Ay%29=2528-4256 ALIGN=MIDDLE  ALT=\"%282800%2Ax-2800%2Ax%29%2B%282000%2Ay-5600%2Ay%29=2528-4256\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282800-2800%29%2Ax%2B%282000-5600%29y=2528-4256 ALIGN=MIDDLE  ALT=\"%282800-2800%29%2Ax%2B%282000-5600%29y=2528-4256\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%282800%2B-2800%29%2Ax%2B%282000-5600%29%2Ay=2528-4256 ALIGN=MIDDLE  ALT=\"cross%282800%2B-2800%29%2Ax%2B%282000-5600%29%2Ay=2528-4256\"   DISABLED_style= \"max-width:90%; height:auto;\" > Notice the x coefficients add to zero and cancel out. This means we've eliminated x altogether.<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  So after adding and canceling out the x terms we're left with:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3600%2Ay=-1728 ALIGN=MIDDLE  ALT=\"-3600%2Ay=-1728\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1728%2F-3600 ALIGN=MIDDLE  ALT=\"y=-1728%2F-3600\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3600 ALIGN=MIDDLE  ALT=\"-3600\"   DISABLED_style= \"max-width:90%; height:auto;\" > to solve for y<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=12%2F25 ALIGN=MIDDLE  ALT=\"y=12%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce<BR>\n" );
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document.write( "  Now plug this answer into the top equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=700%2Ax%2B500%2Ay=632 ALIGN=MIDDLE  ALT=\"700%2Ax%2B500%2Ay=632\"   DISABLED_style= \"max-width:90%; height:auto;\" > to solve for x<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=700%2Ax%2B500%2812%2F25%29=632 ALIGN=MIDDLE  ALT=\"700%2Ax%2B500%2812%2F25%29=632\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=12%2F25 ALIGN=MIDDLE  ALT=\"y=12%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=700%2Ax%2B6000%2F25=632 ALIGN=MIDDLE  ALT=\"700%2Ax%2B6000%2F25=632\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=700%2Ax%2B240=632 ALIGN=MIDDLE  ALT=\"700%2Ax%2B240=632\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=700%2Ax=632-240 ALIGN=MIDDLE  ALT=\"700%2Ax=632-240\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240 ALIGN=MIDDLE  ALT=\"240\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=700%2Ax=392 ALIGN=MIDDLE  ALT=\"700%2Ax=392\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the terms on the right side<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28%281%2F700%29%28700%29%29%2Ax=%28392%29%281%2F700%29 ALIGN=MIDDLE  ALT=\"cross%28%281%2F700%29%28700%29%29%2Ax=%28392%29%281%2F700%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F700 ALIGN=MIDDLE  ALT=\"1%2F700\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This will cancel out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=700 ALIGN=MIDDLE  ALT=\"700\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the left side.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=14%2F25 ALIGN=MIDDLE  ALT=\"x=14%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the terms on the right side<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  So our answer is <BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=14%2F25 ALIGN=MIDDLE  ALT=\"x=14%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=12%2F25 ALIGN=MIDDLE  ALT=\"y=12%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  which also looks like<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2F25 ALIGN=MIDDLE  ALT=\"14%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F25 ALIGN=MIDDLE  ALT=\"12%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Notice if we graph the equations (if you need help with graphing, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Linear-equations/graphing-linear-equations.solver>solver</a>)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=700%2Ax%2B500%2Ay=632 ALIGN=MIDDLE  ALT=\"700%2Ax%2B500%2Ay=632\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400%2Ax%2B800%2Ay=608 ALIGN=MIDDLE  ALT=\"400%2Ax%2B800%2Ay=608\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  we get <BR>\n" );
document.write( "  <BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A++drawing%28+500%2C+600%2C+-10.56%2C+10.56%2C+-10.48%2C+10.48%2C%0D%0A++++graph%28+500%2C+600%2C+-10.56%2C+10.56%2C+-10.48%2C+10.48%2C+%28632-700%2Ax%29%2F500%2C+%28608-400%2Ax%29%2F800+%29%2C%0D%0A++++blue%28++circle%28+0.56%2C+0.48%2C+0.1408+%29+%29+%0D%0A++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=700%2Ax%2B500%2Ay=632 ALIGN=MIDDLE  ALT=\"700%2Ax%2B500%2Ay=632\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400%2Ax%2B800%2Ay=608 ALIGN=MIDDLE  ALT=\"400%2Ax%2B800%2Ay=608\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green) (hint: you may have to solve for y to graph these) and the intersection of the lines (blue circle).<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  and we can see that the two equations intersect at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2F25 ALIGN=MIDDLE  ALT=\"14%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F25 ALIGN=MIDDLE  ALT=\"12%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >). This verifies our answer.</TD></TR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=14%2F25 ALIGN=MIDDLE  ALT=\"x=14%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" > this means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.56 ALIGN=MIDDLE  ALT=\"x=0.56\"   DISABLED_style= \"max-width:90%; height:auto;\" > (just convert to decimal form). So the price of a cream filled donut is $0.56 or 56 cents\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=12%2F25 ALIGN=MIDDLE  ALT=\"y=12%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" > this means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0.48 ALIGN=MIDDLE  ALT=\"y=0.48\"   DISABLED_style= \"max-width:90%; height:auto;\" > (just convert to decimal form). So the price of a jelly donut is $0.48 or 48 cents<BR>\n" );
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