document.write( "Question 117882: In planning for a new item, a manufacturer assumes that the number of items produced x and the cost in dollars C of producing these items are related by a linear equation. Projections are that 100 items will cost $10,000 to produce and that 300 items will cost $22,000 to produce. Find the equation that relates C and x. \n" ); document.write( "

Algebra.Com's Answer #85869 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Basically, $\"C+=+f%28x%29\"$ and $\"f%28x%29\"$ is linear (straight line)
\n" ); document.write( "The general equation for a straight line is $\"y+=+mx+%2B+b\"$
\n" ); document.write( "where $\"m\"$ is the slope and $\"b\"$ is the y-intercept. How
\n" ); document.write( "can I modify this general equation for use in this problem?
\n" ); document.write( " $\"C\"$ will take the place of $\"y\"$ . I will have to find out
\n" ); document.write( "values for $\"m\"$ and $\"b\"$ based on data given.
\n" ); document.write( " $\"C+=+mx+%2B+b\"$
\n" ); document.write( " $\"10000+=+100m+%2B+b\"$
\n" ); document.write( " $\"22000+=+300m+%2B+b\"$
\n" ); document.write( "This is 2 equation and 2 unknowns, so I can solve it
\n" ); document.write( "Multiply the 1st by $\"3\"$ and subtract the 2nd from the 1st
\n" ); document.write( " $\"30000+=+300m+%2B+3b\"$
\n" ); document.write( " $\"22000+=+300m+%2B+b\"$
\n" ); document.write( " $\"8000+=+2b\"$
\n" ); document.write( " $\"b+=+4000\"$
\n" ); document.write( "Substitute this into the 1st
\n" ); document.write( " $\"10000+=+100m+%2B+4000\"$
\n" ); document.write( " $\"100m+=+6000\"$
\n" ); document.write( " $\"m+=+60\"$
\n" ); document.write( "Plugging $\"m\"$ and $\"b\"$ back into the general equation,
\n" ); document.write( " $\"C+=+60x+%2B+4000\"$ answer
\n" ); document.write( "check answer
\n" ); document.write( "Does this equation work with given data?
\n" ); document.write( " $\"C+=+60x+%2B+4000\"$
\n" ); document.write( " $\"10000+=+60%2A100+%2B+4000\"$
\n" ); document.write( " $\"10000+=+6000+%2B+4000\"$
\n" ); document.write( " $\"10000+=+10000\"$
\n" ); document.write( "OK
\n" ); document.write( " $\"22000+=+60%2A300+%2B+4000\"$
\n" ); document.write( " $\"22000+=+18000+%2B+4000\"$
\n" ); document.write( " $\"22000+=+22000\"$
\n" ); document.write( "OK\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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