document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=75454>Question 75454</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you have two numbers. The difference of the two numbers is 12. The product of the two numbers is 17. Multiply the larger of the two numbers by 100, add 50 times the smaller number to that, round the total to the nearest whole number and thats the answer.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54155 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=54155\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=larger number<BR>\n" );
document.write( "And y=smaller number\r<BR>\n" );
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document.write( "Now we are told that:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y=12 ALIGN=MIDDLE  ALT=\"x-y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >----------------------------------eq 1<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Ay=17 ALIGN=MIDDLE  ALT=\"x%2Ay=17\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----------------eq 2\r<BR>\n" );
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document.write( "We can see from a quick inspection that these two numbers are not going to be whole numbers\r<BR>\n" );
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document.write( "From eq 2, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=17%2Fx ALIGN=MIDDLE  ALT=\"y=17%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Substitute this value into  eq 1 and we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-17%2Fx=12 ALIGN=MIDDLE  ALT=\"x-17%2Fx=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >  multiply each term by x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-17=12x ALIGN=MIDDLE  ALT=\"x%5E2-17=12x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  subtract 12x from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-12x-17=0 ALIGN=MIDDLE  ALT=\"x%5E2-12x-17=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > we will solve using the quadratic formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   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=x+=+%2812+%2B-+sqrt%28+144%2B68+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%2812+%2B-+sqrt%28+144%2B68+%29%29%2F%282%29+\"   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=x+=+%2812+%2B-+sqrt%28+212+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%2812+%2B-+sqrt%28+212+%29%29%2F%282%29+\"   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=x+=+%2812+%2B-+14.5602%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%2812+%2B-+14.5602%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2812+%2B14.5602%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%2812+%2B14.5602%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2826.5602%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%2826.5602%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=13.2801 ALIGN=MIDDLE  ALT=\"x=13.2801\"   DISABLED_style= \"max-width:90%; height:auto;\" >----------------------------larger number<BR>\n" );
document.write( "We'll forget about the negative value for x because the positive value works<BR>\n" );
document.write( "ON SECOND THOUGHT, WE NEED TO LOOK AT THE NEGATIVE VALUE FOR X BECAUSE THIS SOLUTION WILL YIELD A DIFFERENT ANSWER.  SEE BELOW:\r<BR>\n" );
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document.write( "substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=13.2801 ALIGN=MIDDLE  ALT=\"x=13.2801\"   DISABLED_style= \"max-width:90%; height:auto;\" > into eq 1 and we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13.2801-y=12 ALIGN=MIDDLE  ALT=\"13.2801-y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >  subtract 13.2801 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y=-1.2801 ALIGN=MIDDLE  ALT=\"-y=-1.2801\"   DISABLED_style= \"max-width:90%; height:auto;\" >  multiply both sides by -1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1.2801 ALIGN=MIDDLE  ALT=\"y=1.2801\"   DISABLED_style= \"max-width:90%; height:auto;\" >---------------------------------smaller number<BR>\n" );
document.write( "CK<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2813.2801%29%281.2801%29=17 ALIGN=MIDDLE  ALT=\"%2813.2801%29%281.2801%29=17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17=17 ALIGN=MIDDLE  ALT=\"17=17\"   DISABLED_style= \"max-width:90%; height:auto;\" > close enough<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13.2801-1.2801=12 ALIGN=MIDDLE  ALT=\"13.2801-1.2801=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12=12 ALIGN=MIDDLE  ALT=\"12=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply the larger number by 100 and we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2813.2801%29%28100%29=1328.01 ALIGN=MIDDLE  ALT=\"%2813.2801%29%28100%29=1328.01\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "50 times the smaller number is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2850%29%281.2801%29=64.005 ALIGN=MIDDLE  ALT=\"%2850%29%281.2801%29=64.005\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now add these two numbers together and round to the nearest whole number:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1328.01%2B64.005=1392.015 ALIGN=MIDDLE  ALT=\"1328.01%2B64.005=1392.015\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Rounded to the nearest whole number we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1392 ALIGN=MIDDLE  ALT=\"1392\"   DISABLED_style= \"max-width:90%; height:auto;\" >---------------------------------------------------answer!!! if I didn't make a mistake\r<BR>\n" );
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document.write( "NOW WE WILL LOOK AT THE NEGATIVE VALUE FOR X:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2812+-+14.5602%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%2812+-+14.5602%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2812+-+14.5602%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%2812+-+14.5602%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2.5602%2F2=-1.2801 ALIGN=MIDDLE  ALT=\"x=-2.5602%2F2=-1.2801\"   DISABLED_style= \"max-width:90%; height:auto;\" >--------------------------larger number\r<BR>\n" );
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document.write( "Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1.2801 ALIGN=MIDDLE  ALT=\"x=-1.2801\"   DISABLED_style= \"max-width:90%; height:auto;\" > into eq 1:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1.2801-y=12 ALIGN=MIDDLE  ALT=\"-1.2801-y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >  add 1.2801 to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y=12%2B1.2801=13.2801 ALIGN=MIDDLE  ALT=\"-y=12%2B1.2801=13.2801\"   DISABLED_style= \"max-width:90%; height:auto;\" >  multiply both sides by -1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-13.2801 ALIGN=MIDDLE  ALT=\"y=-13.2801\"   DISABLED_style= \"max-width:90%; height:auto;\" >-------------------------------------------smaller number\r<BR>\n" );
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document.write( "So now we have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28100%29%28-1.2801%29%2B%2850%29%28-13.2801%29 ALIGN=MIDDLE  ALT=\"%28100%29%28-1.2801%29%2B%2850%29%28-13.2801%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which equals<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-128.01-664.005=-792.015 ALIGN=MIDDLE  ALT=\"-128.01-664.005=-792.015\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-792 ALIGN=MIDDLE  ALT=\"-792\"   DISABLED_style= \"max-width:90%; height:auto;\" >------------------------another answer\r<BR>\n" );
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document.write( "Hope this helps----ptaylor\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );