document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196258>Question 1196258</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The manager of a restaurant found that the cost to produce 50 cups of coffee is<BR>\n" );
document.write( " $ 9.00​, while the cost to produce 350 cups is ​$39.00. Assume the relationship between the cost y to produce x cups of coffee is linear.\r<BR>\n" );
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document.write( "a. Write a linear equation that expresses the​ cost, y, in terms of the number of cups of​ coffee, x.\r<BR>\n" );
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document.write( "b.  How many cups of coffee are produced if the cost of production is ​$ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #829005 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=829005\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "x = number of cups of coffee<BR>\n" );
document.write( "y = total cost in dollars\r<BR>\n" );
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document.write( "50 cups cost $9, meaning: x = 50 and y = 9<BR>\n" );
document.write( "I.e. the point (x,y) = (50, 9) is on the line\r<BR>\n" );
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document.write( "Another point is (350, 39) since 350 cups cost $39 to produce.\r<BR>\n" );
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document.write( "Let's find the slope of the line through (50,9) and (350,39)<BR>\n" );
document.write( "(x1,y1) = (50,9) and (x2,y2) = (350,39)<BR>\n" );
document.write( "m = (y2 - y1)/(x2 - x1)<BR>\n" );
document.write( "m = (39 - 9)/(350 - 50)<BR>\n" );
document.write( "m = 30/300<BR>\n" );
document.write( "m = 1/10<BR>\n" );
document.write( "m = 0.10\r<BR>\n" );
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document.write( "The slope of 0.10 means that each time x goes up by 1, y increases by 0.10<BR>\n" );
document.write( "Each new cup of coffee costs $0.10, i.e. 10 cents\r<BR>\n" );
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document.write( "Now apply point slope form.<BR>\n" );
document.write( "y - y1 = m(x - x1)<BR>\n" );
document.write( "y - 9 = 0.10(x - 50)<BR>\n" );
document.write( "y - 9 = 0.10x - 0.10*50<BR>\n" );
document.write( "y - 9 = 0.10x - 5<BR>\n" );
document.write( "y = 0.10x - 5+9<BR>\n" );
document.write( "y = 0.10x + 4\r<BR>\n" );
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document.write( "The equation is in y = mx+b form<BR>\n" );
document.write( "m = 0.10 = slope<BR>\n" );
document.write( "b = 4 = y intercept\r<BR>\n" );
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document.write( "The slope tells us how much each extra cup costs<BR>\n" );
document.write( "The y intercept is the starting cost. If zero cups are produced, there is still a fixed fee of $4 to set everything up. Think of it like a fee to get in the door.\r<BR>\n" );
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document.write( "All of the work/steps shown above apply to part (a) only.\r<BR>\n" );
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document.write( "Part (b) cannot be answered since the cost of production has been cut off. <BR>\n" );
document.write( "You'll need to revise your post to include this value.\r<BR>\n" );
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document.write( "I'll go over a hypothetical example<BR>\n" );
document.write( "Let's say the cost of production is $100\r<BR>\n" );
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document.write( "This means we plug in y = 100 and solve for x.<BR>\n" );
document.write( "y = 0.10x + 4<BR>\n" );
document.write( "0.10x + 4 = y<BR>\n" );
document.write( "0.10x + 4 = 100<BR>\n" );
document.write( "0.10x = 100-4<BR>\n" );
document.write( "0.10x = 96<BR>\n" );
document.write( "x = 96/(0.10)<BR>\n" );
document.write( "x = 960<BR>\n" );
document.write( "Therefore, a production cost of $100 means that 960 cups were produced.\r<BR>\n" );
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document.write( "Once again, this is a hypothetical example. Follow steps similar to this with the actual cost your teacher gave you.<BR>\n" );
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