A packaging company has been offered a contract to create gift boxes for perfume/cologne. The company needs to buy a special machine to make the boxes. The machine costs $3,000, and each box costs $2 for labor and materials. The perfume/cologne maker as agreed to buy each box for $5. (5 points) 6.) Use this space to show your work for solving this system of equations. Make sure to show all the steps necessary to solve the system of equations. (5 points)

1 answer

Let's denote the number of boxes as "x".

The cost of the machine is $3000.

The cost of labor and materials for each box is $2.

The selling price for each box is $5.

The revenue from selling x boxes is 5x.

The cost of producing x boxes is 2x.

To determine the number of boxes needed to break even, we need to find the value of x for which the revenue equals the cost.

Revenue = Cost

5x = 3000 + 2x

To solve for x, we need to isolate the variable.

Subtracting 2x from both sides:

5x - 2x = 3000

3x = 3000

Dividing both sides by 3:

3x/3 = 3000/3

x = 1000

Therefore, the company needs to sell 1000 boxes to break even.