document.write( "Question 726707: The cost of producing 20 cakes is $315, while 35 cakes is $495. \r
\n" ); document.write( "\n" ); document.write( "(a)Find the linear cost equation
\n" ); document.write( "(b)What is the y-intercept and interpret the answer?
\n" ); document.write( "(c)What is the gradient and interpret the answer?
\n" ); document.write( "(d)Find the cost of producing 55 cakes
\n" ); document.write( "(e)How many cakes can be produced with $1000. \r
\n" ); document.write( "\n" ); document.write( "This was a practice question from a revision test for an exam. If you could, could you please answer this question ASAP, as my exam is in a couple of days. This would be greatly appreciated. Thank you very much :) \n" ); document.write( "
Algebra.Com's Answer #444745 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
The cost of producing 20 cakes is $315, while 35 cakes is $495.
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document.write( "Let x = the number of cakes produced\r\n" );
document.write( "Let y = the cost of preparing those x cakes.\r\n" );
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\n" ); document.write( "The cost of producing 20 cakes is $315,
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document.write( "When x = 20, y = 315, indicated by the ordered pair (20,315) \r\n" );
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\n" ); document.write( "while 35 cakes is $495
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\r\n" );
document.write( "When x = 35, y = 495, indicated by the ordered pair (35,495)\r\n" );
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\n" ); document.write( " (a)Find the linear cost equation
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document.write( "That is the same as the equation of the line that goes through\r\n" );
document.write( "the points (20,315) and (35,495)\r\n" );
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document.write( "We use the slope (gradient) formula:\r\n" );
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document.write( "m = \"%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"\r\n" );
document.write( "where (x1,y1) = (20,315)\r\n" );
document.write( "and where (x2,y2) = (35,495)\r\n" );
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document.write( "m = \"%28495-315%29%2F%2835-20%29\" = \"180%2F15\" = 12\r\n" );
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document.write( "Then we use the point-slope (or point-gradient) formula:\r\n" );
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document.write( "y - y1 = m(x - x1)\r\n" );
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document.write( "m = \"%28495-315%29%2F%2835-20%29\" = \"180%2F15\" = 12\r\n" );
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document.write( "y - 315 = 12(x - 20)\r\n" );
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document.write( "y - 315 = 12x - 240\r\n" );
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document.write( "      y = 12x + 75\r\n" );
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\n" ); document.write( " (b)What is the y-intercept and interpret the answer?
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document.write( "The y intercept is when x = 0\r\n" );
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document.write( "      y = 12x + 75\r\n" );
document.write( "      y = 12(0) + 75\r\n" );
document.write( "      y = 0 + 75\r\n" );
document.write( "      y = 75\r\n" );
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document.write( "So the y-intercept is (0,75).  That means that when\r\n" );
document.write( "no (x=0) cakes have yet been produced, the fixed costs are \r\n" );
document.write( "$75, just for setting up and going into the business\r\n" );
document.write( "of producing cakes.\r\n" );
document.write( "

\n" ); document.write( " (c)What is the gradient and interpret the answer?
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\r\n" );
document.write( "The slope or gradient is m=12.  That means that the cost\r\n" );
document.write( "per cake increases by $12 per cake.\r\n" );
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\n" ); document.write( " (d)Find the cost of producing 55 cakes
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document.write( "We substitute x=55 into \r\n" );
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document.write( "      y = 12x + 75\r\n" );
document.write( "      y = 12(55) + 75\r\n" );
document.write( "      y = 660 + 75\r\n" );
document.write( "      y = 735\r\n" );
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document.write( "Answer: $735\r\n" );
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\n" ); document.write( " (e)How many cakes can be produced with $1000.
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document.write( "We substitute y = 1000 in\r\n" );
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document.write( "      y = 12x + 75\r\n" );
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document.write( "and solve for x:\r\n" );
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document.write( "   1000 = 12x + 75\r\n" );
document.write( "    925 = 12x \r\n" );
document.write( " 77.083 = x, round down to 77.\r\n" );
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document.write( "Answer:  77 cakes can be produced for $1000    \r\n" );
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document.write( "Edwin
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