document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=304318>Question 304318</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (substitution method word problem): One machine has a fixed daily cost of $50 and a variable cost of $1.50 per item produced, wheras a second machine has a fixed daily cost of $10 and a variable cost of $2 per item produced. Using y to represent the total daily costs of these items, determine the number of items x for which the total daily costs will be the same. What is the total daily cost for this number of items? (Use substitution method and steps would be appreciated) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #217999 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=217999\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One machine has a fixed daily cost of $50 and a variable cost of $1.50 per item produced,<BR>\n" );
document.write( " wheras a second machine has a fixed daily cost of $10 and a variable cost of $2 per item produced. <BR>\n" );
document.write( "Using y to represent the total daily costs of these items, determine the number<BR>\n" );
document.write( " of items x for which the total daily costs will be the same.<BR>\n" );
document.write( " What is the total daily cost for this number of items?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write an equation for each statement:<BR>\n" );
document.write( "\"One machine has a fixed daily cost of $50 and a variable cost of $1.50 per item\"<BR>\n" );
document.write( "y = 1.50x + 50<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"a second machine has a fixed daily cost of $10 and a variable cost of $2 per item\"<BR>\n" );
document.write( "y = 2x + 10<BR>\n" );
document.write( ":<BR>\n" );
document.write( "determine the number of items x for which the total daily costs will be the same.<BR>\n" );
document.write( "2nd machine cost = 1st machine cost<BR>\n" );
document.write( "2x + 10 = 1.50x + 50<BR>\n" );
document.write( "2x - 1.50x = 50 - 10<BR>\n" );
document.write( ".5x = 40<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2F.5 ALIGN=MIDDLE  ALT=\"40%2F.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 80 items the cost for each machine is the same<BR>\n" );
document.write( ":<BR>\n" );
document.write( " What is the total daily cost for this number of items?<BR>\n" );
document.write( "Substitute 80 for x in each equation<BR>\n" );
document.write( "y = 1.50(80) + 50<BR>\n" );
document.write( "y = 120 + 50<BR>\n" );
document.write( "y = $170 daily cost, 1st machine<BR>\n" );
document.write( "prove this using the 2nd equation<BR>\n" );
document.write( "y = 2(80) + 10<BR>\n" );
document.write( "y = 160 + 10<BR>\n" );
document.write( "y = $170 daily cost using the 2n machine </SPAN>\n" );
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