document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=211973>Question 211973</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mike bought some kilograms of apples and some kilograms of oranges and spent <BR>\n" );
document.write( "$27.25. The apples cost $3.10 per kilogram and oranges cost $4.95 per kilogram. <BR>\n" );
document.write( "If apples become $1.55 more expensive and oranges become $1.15 chaper he will<BR>\n" );
document.write( "spend $30. How many ograms of apples and oranges did Mike buy? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #160107 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=160107\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Mike bought some kilograms of apples and some kilograms of oranges and spent <BR>\n" );
document.write( "$27.25. The apples cost $3.10 per kilogram and oranges cost $4.95 per kilogram. <BR>\n" );
document.write( "If apples become $1.55 more expensive and oranges become $1.15 cheaper he will<BR>\n" );
document.write( "spend $30. How many kilograms of apples and oranges did Mike buy?\r<BR>\n" );
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document.write( "1.  Let x=number of kilograms of apples  and y=number of kilograms of oranges. \r<BR>\n" );
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document.write( "2.  Cost of apples = x*$3.10 =3.10x\r<BR>\n" );
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document.write( "3.  Cost of oranges= y*4.95=4.95y\r<BR>\n" );
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document.write( "4.  Total cost = 27.25 = 3.10x+4.95y\r<BR>\n" );
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document.write( "5.  Let's look at \"If apples become $1.55 more expensive and oranges become $1.15 cheaper he will spend $30.\"\r<BR>\n" );
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document.write( "    a.  For apples 3.10+1.55=4.65\r<BR>\n" );
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document.write( "    b.  For oranges 4.95-1.15=3.80\r<BR>\n" );
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document.write( "    c.  New total cost = 30 = 4.65x+3.80y\r<BR>\n" );
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document.write( "    d.  Note we still have the same number of apples x and oranges y.\r<BR>\n" );
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document.write( "6.  So now we have two equations and two unknowns\r<BR>\n" );
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document.write( "a.  27.25 = 3.10x+4.95y\r<BR>\n" );
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document.write( "b.  30 = 4.65x+3.80y\r<BR>\n" );
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document.write( "Need to solve for x and y.  The steps below will show x=4 and y=3\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=linear_substitution.solver>SOLVE linear system by SUBSTITUTION</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Solve:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++3.1%5Cx+%2B+4.95%5Cy+=+27.25%2C%0D%0A++++4.65%5Cx+%2B+3.8%5Cy+=+30+%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving 4.95*y to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.1%2Ax+=+27.25+-+4.95%2Ay ALIGN=MIDDLE  ALT=\"3.1%2Ax+=+27.25+-+4.95%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+27.25%2F3.1+-+4.95%2Ay%2F3.1 ALIGN=MIDDLE  ALT=\"x+=+27.25%2F3.1+-+4.95%2Ay%2F3.1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute that<BR>\n" );
document.write( "  into another equation:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.65%2A%2827.25%2F3.1+-+4.95%2Ay%2F3.1%29+%2B+3.8%5Cy+=+30 ALIGN=MIDDLE  ALT=\"4.65%2A%2827.25%2F3.1+-+4.95%2Ay%2F3.1%29+%2B+3.8%5Cy+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=3. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+27.25%2F3.1+-+4.95%2Ay%2F3.1 ALIGN=MIDDLE  ALT=\"x+=+27.25%2F3.1+-+4.95%2Ay%2F3.1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=4.<BR>\n" );
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document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=4%2C+y=3+%29 ALIGN=MIDDLE  ALT=\"system%28+x=4%2C+y=3+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "For Step-By-Step Videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra.\r<BR>\n" );
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