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?__
4.) How many boxes does the perfume/cologne maker need to order for the packaging company to break even?__ Boxes
5.) How many boxes does the perfume/cologne maker need to order for the packaging company to make money?__ boxes
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._______________
1) The equation showing the packaging company's cost to make the boxes: Cost = 3000 + 2 x (number of boxes)
2) The equation showing the perfume/cologne maker's cost to purchase the boxes: Cost = 5 x (number of boxes)
3) The solution to this system of equations is when the packaging company's cost to make the boxes equals the perfume/cologne maker's cost to purchase the boxes.
4) To find the number of boxes needed for the packaging company to break even, we equate the two equations:
3000 + 2 x (number of boxes) = 5 x (number of boxes)
Rearranging the equation:
3000 = 3 x (number of boxes)
Dividing both sides by 3:
1000 = number of boxes
Therefore, the perfume/cologne maker needs to order 1000 boxes for the packaging company to break even.
5) To find the number of boxes needed for the packaging company to make money, the perfume/cologne maker's cost to purchase the boxes needs to be greater than the packaging company's cost to make the boxes.
Setting up an inequality:
5 x (number of boxes) > 3000 + 2 x (number of boxes)
Rearranging the inequality:
3 x (number of boxes) > 3000
Dividing both sides by 3:
number of boxes > 1000
Since the number of boxes must be a whole number, the packaging company needs to sell more than 1000 boxes for them to make money.
6) Solution for the system of equations:
To find the number of boxes needed for the packaging company to break even, we equate the two equations:
3000 + 2 x (number of boxes) = 5 x (number of boxes)
Rearranging the equation:
3000 = 3 x (number of boxes)
1000 = number of boxes
Therefore, the perfume/cologne maker needs to order 1000 boxes for the packaging company to break even.