document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1087081>Question 1087081</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cookie company charges $1.50 per cookie, plus a delivery fee of $1.\r<BR>\n" );
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document.write( "Write a function that represents the total price P (in dollars) as a function of c (number of cookies).\r<BR>\n" );
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document.write( "P(c)= \r<BR>\n" );
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document.write( "What is the total cost to purchase 2 cookies and have them delivered?\r<BR>\n" );
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document.write( "P(2)=\r<BR>\n" );
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document.write( "If I have $35, how many cookies can I have delivered?\r<BR>\n" );
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document.write( "c= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #701363 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=701363\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\">I'll write the answers first and explain how I got each answer. \r<BR>\n" );
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document.write( "The function is P(c) = 1.50*c + 1\r<BR>\n" );
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document.write( "When we plug c = 2 into the function we get P(2) = 4 meaning that it costs $4 to deliver 2 cookies\r<BR>\n" );
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document.write( "If you have $35, then you can have c = 22 cookies delivered\r<BR>\n" );
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document.write( "We're told that it costs $1.50 per cookie and there's a flat fee of $1. This means that no matter how many cookies you order, you pay at least $1. If you order c cookies, then it costs 1.50*c dollars on top of the $1 paid in the flat fee. So that's why the first answer is P(c) = 1.50*c + 1\r<BR>\n" );
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document.write( "Once we have the function P(c) = 1.50*c + 1, we replace every copy of c with 2.<BR>\n" );
document.write( "Then we use PEMDAS to evaluate<BR>\n" );
document.write( "P(c) = 1.50*c + 1<BR>\n" );
document.write( "P(2) = 1.50*2 + 1<BR>\n" );
document.write( "P(2) = 3 + 1<BR>\n" );
document.write( "P(2) = 4<BR>\n" );
document.write( "So it costs $4 to deliver 2 cookies\r<BR>\n" );
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document.write( "The last part is where we take things in reverse. Instead of plugging in some number for c, we replace P(c) with a known cost and we solve for c itself. In this case, P(c) = 35 is the cost or budget we set aside. <BR>\n" );
document.write( "So we go from<BR>\n" );
document.write( "P(c) = 1.50*c + 1<BR>\n" );
document.write( "to<BR>\n" );
document.write( "35 = 1.50*c + 1<BR>\n" );
document.write( "Solve for c to get...<BR>\n" );
document.write( "35 = 1.50*c + 1<BR>\n" );
document.write( "35-1 = 1.50*c + 1 - 1<BR>\n" );
document.write( "34 = 1.50*c<BR>\n" );
document.write( "1.50*c = 34<BR>\n" );
document.write( "1.50*c/1.50 = 34/1.50<BR>\n" );
document.write( "c = 22.6666666666667<BR>\n" );
document.write( "Rounding down (not up) to the nearest whole number and we get c = 22. So we can afford to get 22 cookies if the budget is $35. Why do we round down? Because rounding up leads to P(c) being too costly and we go over budget. Look at how<BR>\n" );
document.write( "P(c) = 1.50*c + 1<BR>\n" );
document.write( "P(22) = 1.50*22 + 1<BR>\n" );
document.write( "P(22) = 34<BR>\n" );
document.write( "and we stay under budget but plugging in c = 23 leads to<BR>\n" );
document.write( "P(c) = 1.50*c + 1<BR>\n" );
document.write( "P(23) = 1.50*23 + 1<BR>\n" );
document.write( "P(23) = 35.50<BR>\n" );
document.write( "and we're 50 cents over budget. So c = 23 is too much. The highest amount we can order is c = 22.</font> </SPAN>\n" );
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