document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=601505>Question 601505</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The first snow blower can remove 20 cubic feet per minute, and the second blower can remove 60 cubic feet per minute. <BR>\n" );
document.write( "Write and simplify an expression that gives the number of cubic feet of snow removed in x minutes.<BR>\n" );
document.write( "Find the total number of cubic feet of snow removed in 36 minutes.<BR>\n" );
document.write( "Which expression gives the number of cubic feet of snow removed in x minutes? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #379902 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=379902\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> THE FIFTH GRADER CALCULATIONS:<BR>\n" );
document.write( "To find the amount of snow removed by one snow blower, you multiply the rate by the time the snow blower is working.<BR>\n" );
document.write( "If the first snow blower works for 36 minutes at a rate of 20 cubic feet per minute, the amount of snow removed is<BR>\n" );
document.write( "(20 cu.ft/minute)(36 minutes) = 720 cu.ft<BR>\n" );
document.write( "In x minutes, it would remove<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2Ax=20x ALIGN=MIDDLE  ALT=\"20%2Ax=20x\"   DISABLED_style= \"max-width:90%; height:auto;\" > cubic feet of snow.<BR>\n" );
document.write( "If the second snow blower works for 36 minutes at a rate of 60 cubic feet per minute, the amount of snow removed is<BR>\n" );
document.write( "(60 cu.ft/minute)(36 minutes) = 2160 cu.ft<BR>\n" );
document.write( "In x minutes, it would remove<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2Ax=60x ALIGN=MIDDLE  ALT=\"60%2Ax=60x\"   DISABLED_style= \"max-width:90%; height:auto;\" > cubic feet of snow.<BR>\n" );
document.write( "With the two snow blowers working together, the amount removed in 36 minutes is<BR>\n" );
document.write( "720 cu.ft + 2160 cu.ft = 2880 cu.ft<BR>\n" );
document.write( " <BR>\n" );
document.write( "THE ALGEBRA POINT OF VIEW:<BR>\n" );
document.write( "In algebra, we would write all the calculations in one step as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820%2A36%29%2B%2860%2A36%29 ALIGN=MIDDLE  ALT=\"%2820%2A36%29%2B%2860%2A36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > cubic feet, and we could make someone else calculate for us.<BR>\n" );
document.write( "Many centuries ago, people got sick and tired of writing that many parentheses, and decided to agree on rules for the ORDER OF OPERATIONS, saying that multiplications in between plus signs will be done first, before adding.<BR>\n" );
document.write( "After that, the same calculation was written as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2A36%2B60%2A36 ALIGN=MIDDLE  ALT=\"20%2A36%2B60%2A36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The same calculation can be done more efficiently as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2A36%2B60%2A36=%2820%2B60%29%2A36 ALIGN=MIDDLE  ALT=\"20%2A36%2B60%2A36=%2820%2B60%29%2A36\"   DISABLED_style= \"max-width:90%; height:auto;\" > DISTRIBUTIVE PROPERTY<BR>\n" );
document.write( "we would multiply just once to calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80%2A36=2880 ALIGN=MIDDLE  ALT=\"80%2A36=2880\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "My explanations are surely wordy (and hopefully helpful, while entertaining), but I suspect the most that your teacher expects for the snow removed in 36 minutes is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2820%2A36%2B60%2A36=%2820%2B60%29%2A36=8%2A36=2880%29 ALIGN=MIDDLE  ALT=\"highlight%2820%2A36%2B60%2A36=%2820%2B60%29%2A36=8%2A36=2880%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "ABOUT THAT DISTRIBUTIVE PROPERTY:<BR>\n" );
document.write( "The concrete details of the case are different, but the abstract math part of the calculation is the same as the case of two pieces of 36-inch wide fabric, with lengths 20 and 60 inches. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing+%28300%2C150%2C-30%2C70%2C-5%2C40%2C%0D%0Arectangle%28-20%2C0%2C60%2C36%29%2Cline%280%2C0%2C0%2C36%29%2C%0D%0Alocate%28-25%2C20%2C36%29%2C%0D%0Alocate%28-12%2C36%2C20%29%2Clocate%2828%2C36%2C60%29%2C%0D%0Alocate%2818%2C-0.3%2C80%29%2C%0D%0Aarrow%2817.5%2C-3%2C-20%2C-3%29%2Carrow%2823%2C-3%2C60%2C-3%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > We can multiply twice to calculate the amount of fabric in each piece and then add to find the total:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2A36%2B60%2A36 ALIGN=MIDDLE  ALT=\"20%2A36%2B60%2A36\"   DISABLED_style= \"max-width:90%; height:auto;\" > square inches of fabric<BR>\n" );
document.write( "or we could add the lengths, and then multiply the total length by the width of the fabric:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820%2B60%29%2A36 ALIGN=MIDDLE  ALT=\"%2820%2B60%29%2A36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The result is the same: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820%2B60%29%2A36=20%2A36%2B60%2A36 ALIGN=MIDDLE  ALT=\"%2820%2B60%29%2A36=20%2A36%2B60%2A36\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " <BR>\n" );
document.write( "AND NOW WITH THAT x:<BR>\n" );
document.write( "In x minutes one blower removes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x ALIGN=MIDDLE  ALT=\"20x\"   DISABLED_style= \"max-width:90%; height:auto;\" > cubic feet of snow, and the other removes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60x ALIGN=MIDDLE  ALT=\"60x\"   DISABLED_style= \"max-width:90%; height:auto;\" > cubic feet of snow.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x%2B60x=%2820%2B60%29x ALIGN=MIDDLE  ALT=\"20x%2B60x=%2820%2B60%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "applying the distributive property.<BR>\n" );
document.write( "When we apply the distributive property that way, we often call the process \"taking out a common factor.\"<BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x%2B60x ALIGN=MIDDLE  ALT=\"20x%2B60x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the first written expression for the problem with x,<BR>\n" );
document.write( "and since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2820x%2B60x=%2820%2B60%29x=80x%29 ALIGN=MIDDLE  ALT=\"highlight%2820x%2B60x=%2820%2B60%29x=80x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80x ALIGN=MIDDLE  ALT=\"80x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the simplified expression to calculate the cubic feet of snow removed in x minutes by two snow blowers with rates of 20 cubic feet per minute and 60 cubic feet per minute. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );