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)
What is the solution to this system of equations?
Let's represent the number of boxes by x.
The cost of the machine is $3,000, so the total cost is $3,000.
The cost of each box, including labor and materials, is $2, so the total cost is $2x.
The perfume/cologne maker agreed to buy each box for $5, so the total revenue is $5x.
We can now set up the equation:
$2x + $3,000 = $5x
To solve this equation, we need to isolate x. We'll start by subtracting $2x from both sides:
$3,000 = $3x
Next, we'll divide both sides by $3 to solve for x:
$3,000/$3 = x
1,000 = x
Therefore, the solution to this system of equations is x = 1,000.
The packaging company needs to make 1,000 gift boxes.