document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=329629>Question 329629</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You are building a landscape garden and want to spend no less than $3,000 and no more than $8,000. You need 35 tons of rock, each costs $60 and each tree costs $99. How many trees can you buy out of a budget of $24,000? Show your answer using inequalities.<BR>\n" );
document.write( "Also want to map (6,15), what is the y-intercept.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #236294 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=236294\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x is what you want to spend.<BR>\n" );
document.write( "3000 <= x <= 8000\r<BR>\n" );
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document.write( "You need 35 tons of rocks.<BR>\n" );
document.write( "Each rock costs $60 and each tree costs $99.\r<BR>\n" );
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document.write( "How many trees can you buy out of a budget of $24,000?\r<BR>\n" );
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document.write( "You need 35 tons of rocks at $60 a ton.\r<BR>\n" );
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document.write( "This means that you need a total of 35 * 60 = $2100 for rocks.\r<BR>\n" );
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document.write( "If you spend $3000 on the garden, then the number of trees you can buy would be equal to $3000 - $2100 / $99 = 9.09..... which rounds out to 9 trees.\r<BR>\n" );
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document.write( "If you spend $8000 on the garden, then the number of trees you can buy would be equal to $8000 - $2100 / $99 = 59.59..... which rounds out to 59 trees.\r<BR>\n" );
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document.write( "Since you do not want to spend less than $3,000 and you do not want to spend more than $8,000 then the fact that you have a budget of $24,000 is irrelevant.\r<BR>\n" );
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document.write( "If you spend as little as $3,000, then $21,000 remains as cash available for future projects.\r<BR>\n" );
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document.write( "If you spend as much as $8,000, then $16,000 remains as cash available for future projects.\r<BR>\n" );
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document.write( "Your formula for the number of trees you can buy would be as follows:\r<BR>\n" );
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document.write( "x >= $3000<BR>\n" );
document.write( "x <= $8000<BR>\n" );
document.write( "budget = $24000<BR>\n" );
document.write( "rocks = $60 * 35 = 2100<BR>\n" );
document.write( "trees = (x - 2100) / 99 truncated to the nearest integer that is less than that value.\r<BR>\n" );
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document.write( "You can graph this as follows:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-1%2C10%2C-10%2C80%2C%281000%2Ax-2100%29%2F99%2C9%2C59%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-1%2C10%2C-10%2C80%2C%281000%2Ax-2100%29%2F99%2C9%2C59%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "On this graph, the value of x is given in thousands.\r<BR>\n" );
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document.write( "3 = 3000<BR>\n" );
document.write( "8 = 8000\r<BR>\n" );
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document.write( "The value of y is the numnber of trees you can buy.\r<BR>\n" );
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document.write( "I set y = 9 and y = 59 to show you that these values occur at around x = 3 and x = 8\r<BR>\n" );
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document.write( "This means that when x = 3000, 9 trees can be bought.\r<BR>\n" );
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document.write( "this also means that when x = 8000, 59 trees can be bought.\r<BR>\n" );
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document.write( "You can plot the number of tree you can buy in between by looking at the graph or by solving the equation for any value of x between 3000 and 8000.\r<BR>\n" );
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document.write( "The equation used to solve is:\r<BR>\n" );
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document.write( "y = (x-2100)/99 truncated to the nearest integer smaller than or equal to y.\r<BR>\n" );
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document.write( "For example:\r<BR>\n" );
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document.write( "When x = 5000, the equation becomes:\r<BR>\n" );
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document.write( "y = (5000 - 2100) / 99 = 29.29..... which truncates to 29.\r<BR>\n" );
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document.write( "Look on the graph and you will see that when y = 29, the value of x is somewhere around 5.\r<BR>\n" );
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document.write( "Here's the graph again, with the value of y = 29 shown.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-1%2C10%2C-10%2C80%2C%281000%2Ax-2100%29%2F99%2C29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-1%2C10%2C-10%2C80%2C%281000%2Ax-2100%29%2F99%2C29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In these graphs, the value of x below 3 and above 8 are irrelevant and not to be considered.\r<BR>\n" );
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document.write( "The equation for how much money is left in the budget would be:\r<BR>\n" );
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document.write( "y = $24000 - x.\r<BR>\n" );
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document.write( "In this case y would equal the money that is left in the budget.\r<BR>\n" );
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document.write( "The graph for the money that is left in the budget is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-1%2C10%2C-10%2C30%2C%2824000+-+1000%2Ax%29%2F1000%2C16%2C21%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-1%2C10%2C-10%2C30%2C%2824000+-+1000%2Ax%29%2F1000%2C16%2C21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In this graph, y represents the amount of money that is left in the budget in thousands of dollars.\r<BR>\n" );
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document.write( "$24,000 equals 24 on the graph\r<BR>\n" );
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document.write( "In this graph, x represents the amount of money that is spent on the project in thousands of dollars.\r<BR>\n" );
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document.write( "$3000 = 3 on the graph<BR>\n" );
document.write( "$8000 = 8 on the graph.\r<BR>\n" );
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document.write( "The only values of x that are relevant would be the values of x from 3 to 8.\r<BR>\n" );
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document.write( "You can see that when x = 3, y = 21 which means that $21,000 is left in the budget after $3000 was spent.\r<BR>\n" );
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document.write( "You can also see that when x = 8, y = 16 which means that $16,000 is left in the budget after $8000 was spent.\r<BR>\n" );
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