document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=468996>Question 468996</A>: <I><SPAN STYLE=\"word-break: break-all;\"> shipping charges at an online bookstore are $4 for one book, $6 for two books and $7 for three to five books. last week, there were 6400 orders of five or fewer books, and a total shipping charges for these orders was $33,600. the number of shipments with $7 charges was 1000 less than the number with $6 charges. how many shipments were made in each category (one book, two books and three to five books)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #321795 by </B><A HREF=/tutors/aboutme.mpl?userid=ccs2011><B>ccs2011(207)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ccs2011><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=ccs2011><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=321795\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let A,B,C be number of shipments for 1-book,2-book,3-book respectively<BR>\n" );
document.write( "The cost of those shipments is 4A, 6B, and 7C respectively<BR>\n" );
document.write( "Given is total number of shipments, total cost, and the fact that C is 1000 less than B.<BR>\n" );
document.write( "Now set up equations:<BR>\n" );
document.write( "A + B + C = 6400<BR>\n" );
document.write( "4A + 6B + 7C = 33,600<BR>\n" );
document.write( "C = B - 1000<BR>\n" );
document.write( "Substitute (B-1000) for C in first 2 equations<BR>\n" );
document.write( "A + B + (B-1000) = 6400<BR>\n" );
document.write( "4A + 6B + 7(B-1000) = 33,600<BR>\n" );
document.write( "Combine like terms<BR>\n" );
document.write( "A + 2B = 7400<BR>\n" );
document.write( "4A + 13B = 40,600<BR>\n" );
document.write( "Now solve for A or B using elimination or substitution method<BR>\n" );
document.write( "I prefer elimination in this case<BR>\n" );
document.write( "Multiply top equation by -4, this will eliminate the A's<BR>\n" );
document.write( "-4A - 8B = -29,600<BR>\n" );
document.write( "4A + 13B = 40,600<BR>\n" );
document.write( "Add equations<BR>\n" );
document.write( "5B = 11,000<BR>\n" );
document.write( "Divide by 5 on both sides<BR>\n" );
document.write( "B = 2200<BR>\n" );
document.write( "Find C by subtracting 1000<BR>\n" );
document.write( "C = 1200<BR>\n" );
document.write( "Find A by subtracting B and C from 6400<BR>\n" );
document.write( "A = 3000 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );