document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120853>Question 1120853</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a customer bought a dozen of pieces of fruits (apples and oranges) for 1.32 dollars. If an apple cost 3 cents more than an orange and more apples than oranges were purchased, how many pieces of each kind were bought? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #736577 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=736577\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "An informal solution by trial and error is of course valid.<br><BR>\n" );
document.write( "But let's look at a formal mathematical process that can be used, along with some logical reasoning, to solve this kind of problem.<br><BR>\n" );
document.write( "Let x be the number of apples; then 12-x is the number of oranges.<BR>\n" );
document.write( "Let y be the cost (in cents) of an apple; the y-3 is the cost of an orange.<br><BR>\n" );
document.write( "The total cost of the fruit (x apples at y cents each, and (12-x) oranges at (y-3) cents each) was $1.32, or 132 cents:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29%28y%29%2B%2812-x%29%28y-3%29+=+132 ALIGN=MIDDLE  ALT=\"%28x%29%28y%29%2B%2812-x%29%28y-3%29+=+132\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy%2B12y-36-xy%2B3x+=+132 ALIGN=MIDDLE  ALT=\"xy%2B12y-36-xy%2B3x+=+132\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12y%2B3x+=+168 ALIGN=MIDDLE  ALT=\"12y%2B3x+=+168\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%2Bx+=+56 ALIGN=MIDDLE  ALT=\"4y%2Bx+=+56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now use some logical reasoning to find exactly the value x must be.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%2Bx+=+56 ALIGN=MIDDLE  ALT=\"4y%2Bx+=+56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+56-4y ALIGN=MIDDLE  ALT=\"x+=+56-4y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4%2814-y%29 ALIGN=MIDDLE  ALT=\"x+=+4%2814-y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "\"14\" and \"y\" are whole numbers, so (14-y) is a whole number.  This equation then tells us that x is a multiple of 4.<br><BR>\n" );
document.write( "But we know x is less than 12; and we know it is greater than (12-x).  The only value of x that satisfies all those conditions is x=8.<br><BR>\n" );
document.write( "So the purchase was of 8 apples and 4 oranges.<br><BR>\n" );
document.write( "The problem doesn't ask for the price of each kind of fruit; but we can go ahead and find them.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%28y%29%2B4%28y-3%29+=+132 ALIGN=MIDDLE  ALT=\"8%28y%29%2B4%28y-3%29+=+132\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8y%2B4y-12+=+132 ALIGN=MIDDLE  ALT=\"8y%2B4y-12+=+132\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12y+=+144 ALIGN=MIDDLE  ALT=\"12y+=+144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+12 ALIGN=MIDDLE  ALT=\"y+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The cost of each apple is y=12 cents; the cost of each orange is y-3 = 9 cents.<br><BR>\n" );
document.write( "Check: 8 apples at 12 cents + 4 oranges at 9 cents = 96 cents + 36 cents = $1.32 </SPAN>\n" );
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