document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203135>Question 1203135</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of two whole numbers is 45 and their difference is less than 10. The number of all possible pairs is: WAN.Algebra.com<BR>\n" );
document.write( "A. 4<BR>\n" );
document.write( "B. 5<BR>\n" );
document.write( "C. 6<BR>\n" );
document.write( "D. 7 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838455 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=838455\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Solving the problem using formal algebra is a bit awkward; and finding a solution using logical reasoning and simple arithmetic is possibly of more benefit.<br><BR>\n" );
document.write( "You need to find how many pairs of whole numbers have a sum of 45 and a difference of less than 10.<br><BR>\n" );
document.write( "So start with the pair of whole numbers with a sum of 45 that has the smallest possible difference.  Simple analysis and simple arithmetic shows that pair to be 23 and 22.<br><BR>\n" );
document.write( "Then find other pairs of whole numbers with a sum of 45 and larger differences by adding 1 to the larger number and subtracting 1 from the smaller number; continue until the difference is greater than 10.<br><BR>\n" );
document.write( "23 and 22 (difference 1)<BR>\n" );
document.write( "24 and 21 (difference 3)<BR>\n" );
document.write( "25 and 20 (difference 5)<BR>\n" );
document.write( "26 and 19 (difference 7)<BR>\n" );
document.write( "27 and 18 (difference 9)<br><BR>\n" );
document.write( "ANSWER: 5 pairs<br><BR>\n" );
document.write( "An observant student will realize that the difference between the two whole numbers will change by 2 from one pair to the next, because you are adding 1 to one of the numbers and subtracting 1 from the other.  So that student will be able to reach the answer of 5 without having to write out all the pairs.<br><BR>\n" );
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document.write( "Final note....<br><BR>\n" );
document.write( "The problem is, technically, not posed correctly.  The number of pairs of whole numbers with a sum of 45 and a difference of less than 10 is much greater than 5.<br><BR>\n" );
document.write( "For example, one such additional pair is 6 and 39.  Their sum is 45, and their difference is 6-39 = -33, which is less than 10.<br><BR>\n" );
document.write( "For the problem to be written correctly, it has to say that the difference of the two numbers is A WHOLE NUMBER less than 10.<br><BR>\n" );
document.write( "Note that the other tutor, in making his list of pairs, stopped when the difference between the two whole numbers became negative, saying that he stopped because negative integers are not whole numbers.<br><BR>\n" );
document.write( "But the statement of the problem didn't say that the difference had to be a whole number....<br>\r<BR>\n" );
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