SOLUTION: Victoria is making a box for her Valentine party at school. The rectangular base of a box has a perimeter of 2 feet. The base is twice as long as it is wide. The box is 5 inches
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Question 1067789: Victoria is making a box for her Valentine party at school. The rectangular base of a box has a perimeter of 2 feet. The base is twice as long as it is wide. The box is 5 inches tall. Victoria plans to cover the top and bottom with red and pink paper, which costs 5 cents per square inch. She then plans to cover the other 4 faces with white paper, which costs 1.5 cents per square inch. How much money will Victoria spend to cover the box with paper? Assume that there is no waste.
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Victoria is making a box for her Valentine party at school.
The rectangular base of a box has a perimeter of 2 feet.
The base is twice as long as it is wide. The box is 5 inches tall.
Victoria plans to cover the top and bottom with red and pink paper, which costs 5 cents per square inch.
She then plans to cover the other 4 faces with white paper, which costs 1.5 cents per square inch.
How much money will Victoria spend to cover the box with paper? Assume that there is no waste.
:
Change the perimeter of the base to inches, 24"
2L + 2w = 24
simplify divide by 2
L + w = 12
"The base is twice as long as it is wide."
L = 2w
Find the dimensions of the base
2w + w = 12
3w = 12
w = 12/3
w = 4" wide, then 8" long
Find the area of the base, then the cost of the paper for top and bottom
8 * 4 * .05 * 2 = $3.20 for top and bottom
:
Find the surface area of the sides, (5" high)
2(8*5) + 2(4*5) = 120 sq/in
Find the cost of the sides
.015 * 120 = $1.80 for the sides
:
Total cost of the box: 3.20 + 1.80 = $5.00
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