A packaging company has been offered a contract to create gift boxes for perume/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.
1.) The equation showing the packaging company's cost to make the
boxes:__
2. The equation showing the perfume/cologne makers cost to purchase the boxes:__
3.) What is the solution to this system of equations?__
1.) The equation showing the packaging company's cost to make the boxes is: Cost = 3000 + 2x, where x is the number of boxes made.
2.) The equation showing the perfume/cologne maker's cost to purchase the boxes is: Cost = 5x, where x is the number of boxes purchased.
3.) To find the solution to this system of equations, we need to set the two costs equal to each other and solve for x:
3000 + 2x = 5x
Subtracting 2x from both sides:
3000 = 3x
Dividing both sides by 3:
x = 1000
Therefore, the solution to this system of equations is that the packaging company needs to make and sell 1000 perfume/cologne gift boxes to cover the cost of the special machine.