document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=27818>Question 27818</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How so you solve this problem?  Photoworks.com charges $7.00 forr processing a 24-exsposure roll and $10.00 for processing a 36-expsosure. After Karens photography field trip, she sent 19 rolls of film to photoworks and pid $151 dollars for processing.  How many rolls of each type were processed </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #15152 by </B><A HREF=/tutors/aboutme.mpl?userid=bmauger><B>bmauger(101)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bmauger><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=15152\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a type of problem solved by 2 simultaneous linear equations.  You can tell this because you are trying to solve for two unknowns (# of 36-rolls & # of 24-rolls) Let x = the number of 24-exposure rolls that Karen submits, and y equal the number of 36-rolls submitted.  From the problem, we are told that the total number of rolls is 19. So the number of 24-rolls (x) and the number of 36-rolls (y) must add up to 19. Or:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=19 ALIGN=MIDDLE  ALT=\"x%2By=19\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "But we can't yet solve this for x or y without knowing something more about them. The other part of the problem says she paid $151 for the total. The amount she'll pay for 24 exposure rolls (x) will be $7/roll or 7x. The amount she'll pay for 36-rolls is $10/roll or 10y.  The total she'll pay is the sum of these two amounts, or:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%2B10y=151 ALIGN=MIDDLE  ALT=\"7x%2B10y=151\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we have to solve these equations.  The easiest way is using substitution, so we'll rewrite the first equation for x:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=19 ALIGN=MIDDLE  ALT=\"x%2By=19\"   DISABLED_style= \"max-width:90%; height:auto;\" >subtract y from both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=19-y ALIGN=MIDDLE  ALT=\"x=19-y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we can substitute 19-y for x in the second equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%2B10y=151 ALIGN=MIDDLE  ALT=\"7x%2B10y=151\"   DISABLED_style= \"max-width:90%; height:auto;\" >Substitute:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2819-y%29%2B10y=151 ALIGN=MIDDLE  ALT=\"7%2819-y%29%2B10y=151\"   DISABLED_style= \"max-width:90%; height:auto;\" >Distibute:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=133-7y%2B10y=151 ALIGN=MIDDLE  ALT=\"133-7y%2B10y=151\"   DISABLED_style= \"max-width:90%; height:auto;\" >Rearrange:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=18 ALIGN=MIDDLE  ALT=\"3y=18\"   DISABLED_style= \"max-width:90%; height:auto;\" >Divide:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=6 ALIGN=MIDDLE  ALT=\"y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So she'll process 6 36-exposure rolls, and 19-6= 13 rolls of 24 exposures.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2A7%2B6%2A10=151 ALIGN=MIDDLE  ALT=\"13%2A7%2B6%2A10=151\"   DISABLED_style= \"max-width:90%; height:auto;\" >Check. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );