SOLUTION: Can you help me please! 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

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Question 99226: Can you help me please!
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 eqaution that relates C and x.
Thanks,

Answer by aaaaaaaa(138) About Me  (Show Source):
You can put this solution on YOUR website!
If the equation that determines C is a linear equation, it is of the form C+=+ax+%2B+b
We have that:
10000+=+100a+%2B+b
22000+=+300a+%2B+b
Now it's a simple matter of solving the system. It's pretty easy by elimination:
10000+-+22000+=+100a+-+300a+%2B+b+-+b
-12000+=+-200a
a+=+60
10000+=+6000+%2B+b
b+=+4000
The resulting equation is, therefore:
C+=+60x+%2B+4000