Let's assume the number of gift boxes the packaging company needs to make is "x".
The cost of labor and materials for each box is $2, so the total cost of labor and materials for "x" boxes would be 2x dollars.
The perfume/cologne maker has agreed to buy each box for $5, so the revenue for "x" boxes would be 5x dollars.
The packaging company needs to buy a special machine for $3,000.
Therefore, the equation representing the total cost for the packaging company is:
Total cost = Cost of machine + Cost of labor and materials
Total cost = $3,000 + $2x
Total cost = $3,000 + 2x
The equation representing the total revenue for the packaging company is:
Total revenue = Price per box x Number of boxes
Total revenue = $5x
To find the breakeven point, where the total cost equals the total revenue, we can set the two equations equal to each other:
$3,000 + 2x = $5x
To solve for "x", we'll isolate the variable:
$3,000 = $5x - 2x
$3,000 = $3x
Now, divide both sides of the equation by 3:
$3,000 / $3 = $3x / $3
$x = 1,000
Therefore, the packaging company needs to make and sell 1,000 gift boxes in order to break even.
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)
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. This is 8th grade math so don’t make the answer too complex
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