document.write( "Question 62405: A toaster manufacturer reviewing historical data notices that the number of toasters produced and the cost to produce the toasters is related by a linear equation. The manufacturer forecasts that 10,000 toasters produced will cost $250,000 and 20,000 toasters produced will cost $350,000. Find the equation that relates to the cost versus the number of toasters produced. \n" ); document.write( "
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If the cost and number of toasters are related by a linear equation then equation will be of the form
\n" ); document.write( "Cost = a number times toasters + another number.\r
\n" ); document.write( "\n" ); document.write( "If I use the letter x for the first number and y for the second number then I have two equations using the data in this problem.\r
\n" ); document.write( "\n" ); document.write( "Equation 1: 250 000 = 10 000x + y
\n" ); document.write( "Equation 2: 350 000 = 20 000x + y\r
\n" ); document.write( "\n" ); document.write( "Subtract the first equation from the second equation (which eliminates y from the new equation)
\n" ); document.write( "to get
\n" ); document.write( "100 000 = 10 000x
\n" ); document.write( "Divide both sides of the equation to get x = 10.\r
\n" ); document.write( "\n" ); document.write( "Substitute x = 10 into equation 1 and get
\n" ); document.write( "250 000 = 10 000 * 10 + y
\n" ); document.write( "250 000 = 100 000 + y Subtract 100 000 from each side of the equation
\n" ); document.write( "250 000 - 100 000 = 100 000 - 100 000 + y
\n" ); document.write( "150 000 = y \r
\n" ); document.write( "\n" ); document.write( "So the function linking cost in dollars and toaster numbers is
\n" ); document.write( "Cost = 10*(Number of toasters) + 150 000
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