elaine is stocking a new box that is 24 inches long, 12 inches wide, and 10 inches high. Make a recommendation to elaine regarding a price for this box size. remember that her box supplier charges her 1/2 cent per square inch of surface area for each box explain your answer?
I'm only in the 6th grade I don't understand this.
The box has 6 faces
top and bottom at 24x12
two ends at 12x10
two sides at 24x10
The total area of cardboard needed then is
2*24*12 + 2*12*10 + 2*24*10 = 1296 in^2
Elaine has to pay 1/2 cent per in^2, or $6.48
SO, you need to suggest a price at least that high, so she can make some profit when she sells the box. That would depend on how much her expenses are just for running the store, and how much of her inventory consists of these boxes.
No problem! I'll break it down for you step by step.
First, let's calculate the surface area of the box. To do that, we need to find the areas of all six sides and then add them together. The formula for the surface area of a rectangular prism (like this box) is:
Surface Area = 2 * (length * width + length * height + width * height)
For this specific box, the length is 24 inches, the width is 12 inches, and the height is 10 inches. Plugging those numbers into the formula, we get:
Surface Area = 2 * (24 * 12 + 24 * 10 + 12 * 10)
Now, let's simplify the equation:
Surface Area = 2 * (288 + 240 + 120)
Surface Area = 2 * 648
Surface Area = 1296 square inches
Now that we know the surface area of the box is 1296 square inches, we can determine the cost. The supplier charges 1/2 cent per square inch of surface area. To calculate the cost, we multiply the surface area by the cost per square inch:
Cost = Surface Area * Cost per square inch
Cost = 1296 * 0.005 (since 1/2 cent is equal to 0.005 dollars)
Cost = $6.48
Therefore, I would recommend that Elaine charges $6.48 for this box size based on the pricing set by her box supplier.