document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=263757>Question 263757</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Translate the problem into a pair of linear equations in two variables.Solve the equations using either elimination or substitution.\r<BR>\n" );
document.write( "\n" );
document.write( "Problem:<BR>\n" );
document.write( "A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with 7% cement should he mix with 10 bags of 15.5% cement to produce a mix containing 12% cement?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #194369 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=194369\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (A solution provided by another tutor provides the correct solution by it does not use 2 equations and two variables as the problem specifies.)<br><BR>\n" );
document.write( "We have two unknowns in this problem: The number of bags of 7% cement and the total number of bags used. So<BR>\n" );
document.write( "Let x = the number of bags of 7% cement, and<BR>\n" );
document.write( "y = the total number of bags of 12% cement.<br><BR>\n" );
document.write( "So the equations are:<BR>\n" );
document.write( "x + 10 = y<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.07%2Ax+%2B+0.155%2A10+=+0.12%2Ay ALIGN=MIDDLE  ALT=\"0.07%2Ax+%2B+0.155%2A10+=+0.12%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "With the first equation already solved for y, using the Substitution Method seems easiest. So we'll substitute into the second equation for y:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.07%2Ax+%2B+0.155%2A10+=+0.12%2A%28x%2B10%29 ALIGN=MIDDLE  ALT=\"0.07%2Ax+%2B+0.155%2A10+=+0.12%2A%28x%2B10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we have a one-variable equation to solve. First we'll simplify:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.07x+%2B+1.55+=+0.12x+%2B+1.2 ALIGN=MIDDLE  ALT=\"0.07x+%2B+1.55+=+0.12x+%2B+1.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I'll get rig of the decimals by multiplying both sides by 100:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x+%2B+155+=+12x+%2B+120 ALIGN=MIDDLE  ALT=\"7x+%2B+155+=+12x+%2B+120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Next we'll get the variable on just one side by subtracting 7x from each side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=155+=+5x+%2B+120 ALIGN=MIDDLE  ALT=\"155+=+5x+%2B+120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 120 from each side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35+=+5x ALIGN=MIDDLE  ALT=\"35+=+5x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide both sides by 5:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7+=+x ALIGN=MIDDLE  ALT=\"7+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since the question is how many bags of 7% cement are used and since x is this number, we don't really care about y. The answer to the question is 7.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );