document.write( "Question 1147822: Allie orders candles from an online company that offers flat rate shipping. She placed an order for 4 candles for $35. A few months later, she placed an order for 12 candles for $95. Write an equation to model the total cost for ordering x candles.
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Algebra.Com's Answer #769156 by Theo(13342)\"\" \"About 
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let x equal the number of candles in each shipment.
\n" ); document.write( "if you use straight line equation, then the total cost is equal to y in the following equation:
\n" ); document.write( "y = mx + b
\n" ); document.write( "x is the number of candles in the shipment.
\n" ); document.write( "m is the average change in the cost per candle.
\n" ); document.write( "b is the fixed cost, regardless of the number of candles shipped.
\n" ); document.write( "you have two (x,y) coordinate points from which to calculate m.
\n" ); document.write( "they are (4,35) and (12,95).
\n" ); document.write( "the total cost is 35 when 4 candles are shipped.
\n" ); document.write( "the total cost if 95 when 12 candles are shipped.
\n" ); document.write( "you use these two points to find m.
\n" ); document.write( "m = (y2 - y1) / (x2 - x1)
\n" ); document.write( "let (x1,y1) = (4,35).
\n" ); document.write( "let (x2,y2) = (12,95).
\n" ); document.write( "m = (y2 - y1) / (x2 - x1) = (95 - 35) / (12 - 4) = 60/8.
\n" ); document.write( "formula becomes y = 60/8 * x + b
\n" ); document.write( "to find b, use either point and replace x and y with the values from that point.
\n" ); document.write( "i used (4,35).
\n" ); document.write( "formula becomes 35 = 60/8 * 4 + b
\n" ); document.write( "solve for b to get b = 35 - 60/8 * 4 = 280/8 - 240/8 = (280-240)/8 = 40/8.
\n" ); document.write( "formula becomes y = 60/8 * x + 40/8.
\n" ); document.write( "when x = 4, formula becomes y = 60/8 * 4 + 40/8 = 35.
\n" ); document.write( "when x = 12, formula becomes y = 60/8 * 12 + 40/8 = 95.
\n" ); document.write( "formula looks good.
\n" ); document.write( "your solution is that the formula to model the cost for x candles is:
\n" ); document.write( "y = 60/8 * x + 40/8.
\n" ); document.write( "this formula can be graphed as shown below:
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\n" ); document.write( "the fixed cost for shipping is 5 dollars.
\n" ); document.write( "that's the cost regardless of the number of candles that are shipped.
\n" ); document.write( "the variable cost is equal to 60/8 times the number of candles shipped.
\n" ); document.write( "when 4 candles are shipped, the fixed cost is 5 and the variable cost is 60/8 * 4 = 240/8 = 30 for a total cost of 5 + 30 = 35.
\n" ); document.write( "when 12 candles are shipped, the fixed cost is 5 and the variable cost is 60/8 * 12 = 720/8 = 90 for a total cost of 5 + 90 = 95.
\n" ); document.write( "the fixed cost is the cost when no candles are shipped.
\n" ); document.write( "per the formula this becomes 60/8 * 0 + 5 = 5.
\n" ); document.write( "note that y = 60/8 * x + 40/8 is the same equation as y = 7.5 * x + 5.
\n" ); document.write( "the graph of each of those two equations is the same red line.
\n" ); document.write( "the variable cost means the same as the incremental cost.
\n" ); document.write( "it's the cost for each additional unit sold.\r
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