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Math Help - Area/Cost/Time

  1. #1
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    Area/Cost/Time

    This is definitely one of my weaker areas in math, so any help is appreciated, thanks in advance.

    Kim plans to paint the floor and outside walls of a playhouse that her dad built for her. She also wants to shingle the roof. The house is 9 feet long, 7 feet wide and 8 feet high at the peak, and the walls are 6 feet high. There are four windows (2' by 2' each) one door (5' by 2'). Paint is sold in 4L cans at $24.99 each, and shingles cost $34.99 per bundle. One bundle of shingles covers about 25 square feet, and one 4L can of paint covers 125 square feet. She also needs to buy a brush for $6.99, a roller brush for $10.95 and shingle nails for $4.00.

    A. Draw a sketch of the house showing front and side views. Be sure to show where you would locate the door and the windows.

    B. Determine the area to be painted, and also the cost of painting if she applies two coats of paint.

    C. Determine the area to be shingled, and the total cost of shingling.

    D. How long will she spend painting if she can paint 25 square feet in 15 minutes?

    E. Kim decides to build a small 6' by 5' deck for the house using boards that are 4" wide and cost $0.35 per foot. What is the cost of the deck? (Her dad has given her some materials to build the base of the deck, and she uses the 4" boards to cover the base.)

    F. What is Kim's total cost of painting, shingling and deck building? Be sure to include PST and GST at 7% each.
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  2. #2
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    Okay, so I've attached a bad drawing of what I think the problem is describing. The basic figure is a rectangular prism topped by a rectangular pyramid.

    For part B, you want to determine the area of the floor and outside walls. There is one 9x7 floor, two 6x7 walls, and two 9x6 walls. So

    Area = (9)(7) + 2(6)(7) + 2(9)(6) = 255 ft^2

    However, you have to remember to subtract the area of the door and windows, since they won't be painted. First we calculate the total area of the door and windows - there are four 2x2 windows and one 5x2 door. So

    Area = 4(2)(2) + (5)(2) = 26 ft^2

    Subtracting this area from the total, we get

    Area = 229 ft^2

    which is the area to be painted. To calculate the cost, we first need to find how much paint will be required. We know one can of paint will cover 125 ft, and we need to cover 229 feet. So clearly we will need two cans of paint. Then we add the cost of the paint and brushes: we need 2 cans of paint (24.99 each), a brush (6.99), and a roller brush (10.95). So

    Cost = 2(24.99) + 6.99 + 10.95 = 67.92

    So for part B, you get an area of 229 square feet and a cost of $67.92. Can you go from there?
    Attached Thumbnails Attached Thumbnails Area/Cost/Time-picture-3.png  
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  3. #3
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    Thanks for the help, part D and part F I can figure out and get those on my own, but for part C and part E I'm not sure how to calculate those. Sorry if the answers should be obvious, I'm just not very good at math obviously...
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  4. #4
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    I'm thinking the roof is shaped more like this. Of course, it's impossible to tell without with a picture.



    If so, then to find the area of the roof we'd simply find the length of the hypotenuse of the triangle and multiply it by 2 times the length of the house.

    So,

     7^{2}+8^{2}=c^{2}

    113=c^{2}

    c=\sqrt{113}ft

    And then,

     A=2*9*\sqrt{113}=...ft^{2}
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