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#1 2006-10-04 17:21:35

More lost
Guest

equation

here is the problem.
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.

#2 2006-10-04 23:20:09

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: equation

As the equation is linear, your answer is going to be of the form C = ax + b, and you need to find out what those constants are.

The given information can help you to find these.

100a+b = 10000
300a+b = 22000

Taking the first equation away from the second gives 200a = 12000.

From this we can deduce that a = 60.
Now we know a, we can easily substitute that into one of the original equations to find b.
100*60 + b = 10000
b = 4000.

Therefore, your equation is C = 60a+4000.
Or C = 20(3a+200) if you want to make it a bit neater, but that bit's not necessary.


Why did the vector cross the road?
It wanted to be normal.

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