document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=158201>Question 158201</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0132383578/algebrahomeworkh>Intermediate Algebra for College Students</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Painting Sales: Joseph DeGuizman, an artist, sells both large paintings and small paintings. He sells his small paintings for $60 and his large paintings for $180. At the end of the week he determined that the total amount he made selling 12 paintings was $1200. Determine the number of small and the number of large paintings that he sold.\r<BR>\n" );
document.write( "\n" );
document.write( "---I know the answers, more importantly, I cant understand how to setup the equation(s) to get the answers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #116590 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=116590\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let a = number of small paintings sold<BR>\n" );
document.write( "let b = number of large paintings sold<BR>\n" );
document.write( "let $60*a = amount of money received from the sale of small paintings<BR>\n" );
document.write( "let $180*b = amount of money received from the sale of large paintings<BR>\n" );
document.write( "number of total paintings sold is 12, so<BR>\n" );
document.write( "first equation becomes: a+b=12<BR>\n" );
document.write( "total amount of money made is $1200, so<BR>\n" );
document.write( "second equation becomes: $60*a + $180*b = $1200.<BR>\n" );
document.write( "to solve this equation, you need to remove one of the unknowns by describing it in terms of the other unknown.<BR>\n" );
document.write( "in the first equation, if a+b=12, then a=12-b (subtract b from both sides of the equation).<BR>\n" );
document.write( "in the second equation substitute (12-b) everywhere you see a.<BR>\n" );
document.write( "second equation becomes<BR>\n" );
document.write( "$60*(12-b) + $180*b = $1200<BR>\n" );
document.write( "expanding this becomes<BR>\n" );
document.write( "$60*12 - $60*b + $180*b = $1200<BR>\n" );
document.write( "multiplying out all factors that can be multiplied, this becomes<BR>\n" );
document.write( "$720 - $60*b + $180*b = $1200<BR>\n" );
document.write( "subtracting $720 from both sides of the equation and it becomes<BR>\n" );
document.write( "$180*b - $60*b = $1200 - $720<BR>\n" );
document.write( "adding like terms together, this becomes<BR>\n" );
document.write( "$120*b = $480<BR>\n" );
document.write( "solving for b, this equation becomes<BR>\n" );
document.write( "b=$480/$120 = 4<BR>\n" );
document.write( "if b = 4, then 12-b = 8 = a<BR>\n" );
document.write( "a = 8<BR>\n" );
document.write( "b = 4<BR>\n" );
document.write( "second equation becomes<BR>\n" );
document.write( "$60*8 + $180*4 = $1200, which becomes<BR>\n" );
document.write( "$480 + $720 = $1200, which becomes<BR>\n" );
document.write( "$1200 = $1200 proving the formula is correct with<BR>\n" );
document.write( "a = 8, and<BR>\n" );
document.write( "b = 4\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );