Question 20529
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