document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=263976>Question 263976</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For a certain three digit positive number the ones digit is 3 times the hundreds digit. The tens digit is 1 less than the ones digit. The ones digit is 15 less than the product of the hundreds and tens digit. What digit is the ones digit?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #194441 by </B><A HREF=/tutors/aboutme.mpl?userid=JBarnum><B>JBarnum(2146)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=JBarnum><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=JBarnum><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=194441\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For a certain three digit positive number the ones digit is 3 times the hundreds digit. The tens digit is 1 less than the ones digit. The ones digit is 15 less than the product of the hundreds and tens digit. What digit is the ones digit? \r<BR>\n" );
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document.write( "first take each line by line<BR>\n" );
document.write( "\"For a certain three digit positive number\" means: xyz<BR>\n" );
document.write( "using xyz as the 3 digit number: ones digit= z, tens digit= y, hundreds digit=x <BR>\n" );
document.write( "\"ones digit is 3 times the hundreds digit\"means: z=3x<BR>\n" );
document.write( "\"The tens digit is 1 less than the ones digit\" means: y=z-1<BR>\n" );
document.write( "\"The ones digit is 15 less than the product of the hundreds and tens digit\" means: z=xy-15<BR>\n" );
document.write( "\"What digit is the ones digit?\" means z=?\r<BR>\n" );
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document.write( "since we are looking for z rearange the first equation z=3x to x=z/3 so relist your equations:<BR>\n" );
document.write( "x=z/3  y=z-1  z=xy-15<BR>\n" );
document.write( "we want to find value for z and they give value for y and you just got the value for x, so in the third equation put the z/3 for x and the z-1 for y:<BR>\n" );
document.write( "z=xy-15<BR>\n" );
document.write( "z=((z/3)(z-1))-15 now simplify<BR>\n" );
document.write( "z= ((z^2-z)/3)-15 id get rid of the fraction by multiplying everything by 3<BR>\n" );
document.write( "3z= z^2-z-45  subtract 3z from both sides<BR>\n" );
document.write( "0= z^2-z-45-3z simplify<BR>\n" );
document.write( "0= z^2-4z-45 Standard Quadratic equation A=1 B=-4 C=-45<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=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=az%5E2%2Bbz%2Bc=0 ALIGN=MIDDLE  ALT=\"az%5E2%2Bbz%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1z%5E2%2B-4z%2B-45+=+0 ALIGN=MIDDLE  ALT=\"1z%5E2%2B-4z%2B-45+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"z%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-4%29%5E2-4%2A1%2A-45=196 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-4%29%5E2-4%2A1%2A-45=196\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=196 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--4%2B-sqrt%28+196+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--4%2B-sqrt%28+196+%29%29%2F2%5Ca\"   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=z%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+196+%29%29%2F2%5C1+=+9 ALIGN=MIDDLE  ALT=\"z%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+196+%29%29%2F2%5C1+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5B2%5D+=+%28-%28-4%29-sqrt%28+196+%29%29%2F2%5C1+=+-5 ALIGN=MIDDLE  ALT=\"z%5B2%5D+=+%28-%28-4%29-sqrt%28+196+%29%29%2F2%5C1+=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1z%5E2%2B-4z%2B-45 ALIGN=MIDDLE  ALT=\"1z%5E2%2B-4z%2B-45\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1z%5E2%2B-4z%2B-45+=+1%28z-9%29%2A%28z--5%29 ALIGN=MIDDLE  ALT=\"1z%5E2%2B-4z%2B-45+=+1%28z-9%29%2A%28z--5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 9, -5.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B-45+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B-45+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "To reiterate the question that you gave us to solve\r<BR>\n" );
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document.write( "\"What digit is the ones digit?\"<BR>\n" );
document.write( "I did answer it, check the quadratic equation again (x=9,-5), and since it cant be negative the ones digit must be 9.\r<BR>\n" );
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document.write( "**oh and if you want to know what the other 2 digits are reread the question knowing the ones digit is 9 so we know xy9<BR>\n" );
document.write( "9/3=x x=3 now we know 3y9<BR>\n" );
document.write( "y=9-1=8 now we know 389. but this number isnt the answer to the question you stated above\r<BR>\n" );
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document.write( " </SPAN>\n" );
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