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.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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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