Help me out QR problem!

[vDDmaniaC]

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Another tricky problem.

A painting which is 4ft wide and 5ft long is surrounded by a rectangular frame 6inches wide. What percent of the area of the picture and the frame is ccoupied by the frame?

1. 10.5
2. 20
3. 30
4. 33 1/3
5. 50

Thanks

 

[smile101]

Another tricky problem.

A painting which is 4ft wide and 5ft long is surrounded by a rectangular frame 6inches wide. What percent of the area of the picture and the frame is ccoupied by the frame?

1. 10.5
2. 20
3. 30
4. 33 1/3
5. 50

Thanks

why is this tricky?

 

[vDDmaniaC]

Any explanation? I know the answer. Wonder how to get the answer

 

[tuthluver]

this is how I did it, I could be wrong(never claimed to be good at math):
4ft X 5ft=20
Six inches per each side is an extra foot, so:
5ft X 6ft=30sqft. i the area of the frame and the picture, so now you must minus the picture.

30-20=10

(10/30)X100=33.33%

 

[Simiam]

I got 33.3%...

Picture Alone = 20ft^2
Picture w/ Frame = 30ft^2
% of Frame is (30-20)/ 30 = 33.3%?

 

[Optimism Smiles]

Any explanation? I know the answer. Wonder how to get the answer

First you DRAW A PICTURE! 🙂 Now, convert everything to inches. You get that the painting is 48 in x 60 in. To find the total area, adjust the painting sides to include the frame. The width is 48 inches, but if the frame is 6 inches, the frame will overhang 6 inches of the painting on EACH SIDE. (Look at your picture! 👍 ). This means the width is 48 in + 6 in + 6 in = 60 inches. Do the same for the length. The total length = 60 in + 6 in + 6 in = 72 inches. You know that to get the area of JUST the frame, you can subtract the area of JUST the painting from the TOTAL area. The total area (including frame) is 60 in x 72 in = 4320 in. The area of only the painting itself is 48 in x 60 in = 2880 in. Subtract 4320 - 2880 = 1440 inches (area of only the frame).

Now you want the percentage of the Frame/Total area of frame + painting. This is 1440 in/4320 in = .33333..... = 33 1/3 % 🙂

That is a long way but there is a much faster way to do it: The picture area is 4x5 ft = 20 ft^2. If you add 6 inches to both sides, and you get a total of 1 ft added to each the length and width. Now 5x6 = 30 ft^2. Subtract 30-20 and you get 10 ft from just the frame. Now Just divide 10 ft^2/30 ft^2. Either works!

 

[vDDmaniaC]

Thanks! Optimism! your explanation is really helpful!