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 point
What is the solution to this system of equations?
Let x be the number of gift boxes made.
The cost of the machine is $3000.
The cost for labor and materials per box is $2.
The selling price per box is $5.
The total cost for the machine is $3000.
The total cost for labor and materials is 2x.
The total selling price is 5x.
Setting up the equation for the total cost: 3000 + 2x = 5x
Subtracting 2x from both sides: 3000 = 3x
Dividing both sides by 3: 1000 = x
Therefore, the solution to the system of equations is x = 1000.
How many boxes does the perfume/cologne maker need to order for the packaging company to break even?
To determine the number of boxes the perfume/cologne maker needs to order for the packaging company to break even, we need to find the quantity at which the total cost matches the total selling price.
Let x be the number of gift boxes made.
The cost of the machine is $3000.
The cost for labor and materials per box is $2.
The selling price per box is $5.
The total cost for the machine is $3000.
The total cost for labor and materials is 2x.
The total selling price is 5x.
Setting up the equation for breaking even: 3000 + 2x = 5x
Subtracting 2x from both sides: 3000 = 3x
Dividing both sides by 3: 1000 = x
The perfume/cologne maker needs to order 1000 boxes for the packaging company to break even.
How many boxes does the perfume/cologne maker need to order for the packaging company to make money?
For the packaging company to make money, the total selling price must be higher than the total cost.
Let x be the number of gift boxes made.
The cost of the machine is $3000.
The cost for labor and materials per box is $2.
The selling price per box is $5.
The total cost for the machine is $3000.
The total cost for labor and materials is 2x.
The total selling price is 5x.
Setting up the inequality for making money: 5x > 3000 + 2x
Subtracting 2x from both sides: 3x > 3000
Dividing both sides by 3: x > 1000
The perfume/cologne maker needs to order more than 1000 boxes for the packaging company to make money.