SOLUTION: Could you please help me with this problem? I have a hard time figuring out how to set up word problems... The perimeter of a picture frame is 11 feet. If three times the heig

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Question 171692: Could you please help me with this problem? I have a hard time figuring out how to set up word problems...
The perimeter of a picture frame is 11 feet. If three times the height is equal to eight times the width, what are the dimensions of the frame?
Thank you so much for your help...
Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=width and y=height


"The perimeter of a picture frame is 11 feet" translates to 11=2x%2B2y. Note: remember, the perimeter formula is P=2L%2B2W where L and W are the length and width


"three times the height is equal to eight times the width" translates to 3y=8x


3y=8x Start with the second equation


y=%288x%29%2F3 Divide both sides by 3 to isolate y


11=2x%2B2y Go back to the first equation


11=2x%2B2%28%288x%29%2F3%29 Plug in y=%288x%29%2F3


11=2x%2B%2816x%29%2F3 Multiply


3%2811%29=3%282x%29%2Bcross%283%29%28%2816x%29%2Fcross%283%29%29 Multiply EVERY term by the LCD 3 to clear the fraction.


33=6x%2B16x Multiply and simplify


33=22x Combine like terms.


33%2F22=x Divide both sides by 22 to isolate "x"


3%2F2=x Reduce


So the first answer is x=3%2F2 (which in decimal form is x=1.5)



y=%288x%29%2F3 Go back to the isolated equation


y=%288%283%2F2%29%29%2F3 Plug in x=3%2F2


y=%2812%29%2F3 Multiply 8 and 3%2F2 to get 8%283%2F2%29=24%2F2=12


y=4 Reduce


So the second answer is y=4



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Answer:


So the answers are x=3%2F2 (which in decimal form is x=1.5) and y=4


This means that the width is 1.5 feet and the height is 4 feet.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
All that's needed is the formula for perimeter
Let P= perimeter
Let h= height
Let w= width
To find the perimeter, you start at a certain point
on the closed figure and go all the way around
returning to your starting point
P+=+h+%2B+w+%2B+h+%2B+w
P+=+2h+%2B+2w
Given:
P+=+11ft
3h+=+8w
h+=+%288%2F3%29%2Aw
-----------------
11+=+2h+%2B+2w
11+=+2%2A%288%2F3%29%2Aw+%2B+2w
Multiply both sides by 3
33+=+16w+%2B+6w
22w+=+33
w+=+1.5ft
h+=+%288%2F3%29%2Aw
h+=+%288%2F3%29%2A%283%2F2%29
h+=+4ft
The frame is 4 ft high anf 1.5 ft wide
check:
11+=+2%2A4+%2B+2%2A1.5
11+=+8+%2B+3
11+=+11
OK