document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208927>Question 1208927</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A department store sells a pair of shoes for $73 and an assortment of bags for $44 each. In one day, the store sells n pairs of shoes and (n  -  7) bags. Which expressions represent the day’s total sales for shoes and bags at the store?\r<BR>\n" );
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document.write( "73n + 44n + 308\r<BR>\n" );
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document.write( "44(n  -  7) + 73n\r<BR>\n" );
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document.write( "44n + 73(n  -  7)\r<BR>\n" );
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document.write( "73n + 44(n  -  7)\r<BR>\n" );
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document.write( "n(73 + 44)  -  7\r<BR>\n" );
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document.write( "117n  -  308 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #847457 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=847457\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answers: <BR>\n" );
document.write( "<font color=red>73n + 44(n - 7)</font><BR>\n" );
document.write( "<font color=red>44(n - 7) + 73n</font><BR>\n" );
document.write( "<font color=red>117n - 308</font>\r<BR>\n" );
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document.write( "Reason<BR>\n" );
document.write( "n = number of pairs of shoes<BR>\n" );
document.write( "p = 73n = cost of just those shoes alone, when each pair sells at $73<BR>\n" );
document.write( "n-7 = number of bags<BR>\n" );
document.write( "q = 44(n-7) = cost of just those bags alone, when each bag sells at $44<BR>\n" );
document.write( "shoes + bags = p+q = <font color=red>73n + 44(n - 7)</font> = total cost of shoes and bags<BR>\n" );
document.write( "Since we can add two numbers in any order, it means the order of 44(n-7) and 73n doesn't matter. We can swap the order of p and q.<BR>\n" );
document.write( "Therefore that expression in red is equivalent to <font color=red>44(n - 7) + 73n</font><BR>\n" );
document.write( "When distributing and combining like terms, you'll end up with <font color=red>117n - 308</font>\r<BR>\n" );
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document.write( "A visual way to verify if two algebraic expressions are equivalent is to graph them.<BR>\n" );
document.write( "Consider graphing y = 73x+44(x-7) and y = 117x-308. Both will produce the exact same line. One line is perfectly overlapping the other. <BR>\n" );
document.write( "I recommend using either <a  rel=nofollow HREF=\"https://www.geogebra.org/calculator\">GeoGebra</a> or <a  rel=nofollow HREF=\"https://www.desmos.com/calculator\">Desmos</a> as a graphing tool.<BR>\n" );
document.write( "Make sure that you use x instead of n. <BR>\n" );
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