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)
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.