document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175463>Question 175463</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you want to cover the backyard with decorative rock and plant some trees as the first phase of the project. You need 30 tons of rock to cover the area. If each ton cost $60 and each tree is $84, what is the maximum number of trees you can buy with a budget for rock and trees of $2,500? Write an inequality that illustrates the problem and solver. Express your answer as an inequality and explain how you arrived at your answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130545 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=130545\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=number of trees\r<BR>\n" );
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document.write( "Since \"You need 30 tons of rock\" and \"each ton cost $60\", this means that the total cost of the rocks is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2A60=1800 ALIGN=MIDDLE  ALT=\"30%2A60=1800\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the rocks will cost you $1,800 \r<BR>\n" );
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document.write( "Now because \"each tree is $84\" and we let \"x\" be the number of trees, this means that the total cost of the trees is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=84x ALIGN=MIDDLE  ALT=\"84x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Now add the two costs to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1800%2B84x ALIGN=MIDDLE  ALT=\"1800%2B84x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Rearrange the expression to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=84x%2B1800 ALIGN=MIDDLE  ALT=\"84x%2B1800\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since you have a \"budget for rock and trees of $2,500\", this means that you can spend anything less than or equal to $2,500 (nothing higher). So algebraically, this means that the total cost <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=84x%2B1800 ALIGN=MIDDLE  ALT=\"84x%2B1800\"   DISABLED_style= \"max-width:90%; height:auto;\" > is less than or equal to 2500 like this\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=84x%2B1800%3C=2500 ALIGN=MIDDLE  ALT=\"84x%2B1800%3C=2500\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solving the Inequality:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=84x%2B1800%3C=2500 ALIGN=MIDDLE  ALT=\"84x%2B1800%3C=2500\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=84x%3C=2500-1800 ALIGN=MIDDLE  ALT=\"84x%3C=2500-1800\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1800 ALIGN=MIDDLE  ALT=\"1800\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=84x%3C=700 ALIGN=MIDDLE  ALT=\"84x%3C=700\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=%28700%29%2F%2884%29 ALIGN=MIDDLE  ALT=\"x%3C=%28700%29%2F%2884%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=84 ALIGN=MIDDLE  ALT=\"84\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=25%2F3 ALIGN=MIDDLE  ALT=\"x%3C=25%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=25%2F3 ALIGN=MIDDLE  ALT=\"x%3C=25%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Which approximates to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=8.333 ALIGN=MIDDLE  ALT=\"x%3C=8.333\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "If we round down, we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=8 ALIGN=MIDDLE  ALT=\"x%3C=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that the number of trees is less than or equal to 8. So you can buy at most 8 trees to stay within budget. </SPAN>\n" );
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