document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=48121>Question 48121</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/1565771400/algebrahomeworkh>Algebra 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> This is a Value Word Problems lesson. I learned it in chapter 19 but it doesn't help for my problem. Here it is<BR>\n" );
document.write( "The expensive ones cost $7 each, whereas the worthless ones sold for only $2 each. Monongahela spent $111 and bought three more expensive ones than worthless ones. How may of each kind did she buy.<BR>\n" );
document.write( "THE ANSWER IS 10 WORTHLESS ONES AND 13 EXPENSIVE ONES. I WANT TO KNOW HOW DID THEY GET THAT. \r<BR>\n" );
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document.write( "PLEASE AND THANK YOU </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #31841 by </B><A HREF=/tutors/aboutme.mpl?userid=tutorcecilia><B>tutorcecilia(2152)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=tutorcecilia><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=tutorcecilia><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=31841\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are working with two different variables, x is one variable and y is the other variable.  Since you have two variables, use the following formula:<BR>\n" );
document.write( "Ax + By = C<BR>\n" );
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document.write( "A = rate, cost or percent of A = $7<BR>\n" );
document.write( "x = the amount or number of A = x<BR>\n" );
document.write( "B = rate, cost or percent of B = $2<BR>\n" );
document.write( "y = the amount or number of B = y<BR>\n" );
document.write( "C = the total amount = $111<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Expensive  DISABLED_event_ones=  $7x [We do not know how many expensive items are available]<BR>\n" );
document.write( "Worthless  DISABLED_event_ones=  $2y [We do not know how many worthless items are available]<BR>\n" );
document.write( "Total amount spent = C = $111<BR>\n" );
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document.write( "Ax + By = C [Formula for linear equations]<BR>\n" );
document.write( "7x + 2y = 111 [Plug-in the values]<BR>\n" );
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document.write( "But, there is one more piece of information -- \"...and bought three more expensive ones than worthless ones\".  <BR>\n" );
document.write( "This translate into:<BR>\n" );
document.write( "Number of expensive ones (x) = Number of Worthless ones (y) + 3 more<BR>\n" );
document.write( "x = y + 3 [Substitute this (y + 3) in the equation]<BR>\n" );
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document.write( "7(y+3) + 2y = 111 [Simplify]<BR>\n" );
document.write( "7y + 21 + 2y = 111  [Solve for y]<BR>\n" );
document.write( "9y + 21 = 111<BR>\n" );
document.write( "9y + 21 - 21 = 111 - 21<BR>\n" );
document.write( "9y = 90<BR>\n" );
document.write( "9y/9 = 90/9<BR>\n" );
document.write( "y = 10<BR>\n" );
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document.write( "Plug (y=10) back into the original equation and solve for x]<BR>\n" );
document.write( "7x + 2y = 111<BR>\n" );
document.write( "7x + 2(10) = 111<BR>\n" );
document.write( "7x + 20 = 111<BR>\n" );
document.write( "7x + 20 - 20 = 11 - 20<BR>\n" );
document.write( "7x = 91<BR>\n" );
document.write( "7x/7 = 91/7<BR>\n" );
document.write( "x = 13<BR>\n" );
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document.write( "Check by plugging all of the values back into the original equation.<BR>\n" );
document.write( "7x + 2y = 111<BR>\n" );
document.write( "7(13) + 2(10) = 111<BR>\n" );
document.write( "7(13) + 2(10) = 111<BR>\n" );
document.write( "111 = 111 [Checks out]\r<BR>\n" );
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document.write( " </SPAN>\n" );
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