Question 20529: Claire has a small personal business making scented candles.
Her startup costs are $200. Her cost to make each cangle is
$1.50. She sells each candle for $4.00. Use a system of
equations to determine the number of candles she must sell
to break even. (Write one equation for her prodction costs
and one for her sales revenue.)=
Answer by mmm4444bot(95)   (Show Source):
You can put this solution on YOUR website! Hello There:
Let x = the number of candles produced and sold.
The costs are modeled by this equation:
C = 200 + 1.5*x
because each x costs $1.50, and there is the startup costs (which is fixed one time only) of $200.
The revenue is modeled by this equation:
R = 4*x
because they collect $4 for each x.
To break even means that the costs equal the revenue (i.e., there is no profit, but there is no loss either).
We find this number of candles by setting the costs equal to the revenue.
200 + 1.5*x = 4*x
Subtract 1.5*x from both sides so that we can combine the x-terms together on the right side.
200 = 4*x - 1.5*x
200 = 2.5*x
Solve for x by dividing both sides by 2.5:
x = 200/2.5
x = 80
~ Mark
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