SOLUTION: Henry had a pole measuring 7 m. He painted it red, yellow and black. He painted 1 3/4 of the pole red. The length of the black part was 3/4 of the length of the yellow part. What

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Henry had a pole measuring 7 m. He painted it red, yellow and black. He painted 1 3/4 of the pole red. The length of the black part was 3/4 of the length of the yellow part. What      Log On


   

Question 1205950: Henry had a pole measuring 7 m. He painted it red, yellow and black. He painted
1 3/4 of the pole red. The length of the black part was 3/4 of the length of the
yellow part. What was the length of the pole that was cross(poured) painted black?
Found 4 solutions by mananth, josgarithmetic, Edwin McCravy, greenestamps:
Answer by mananth(16946) About Me  (Show Source):
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Henry had a pole measuring 7 m. He painted it red, yellow and black. He painted 1 3/4 of the pole red. The length of the black part was 3/4 of the length of the yellow part. What was the length of the pole that was poured black?
Henry had a pole measuring 7 m
He painted 1 3/4 of the pole red.
7/4 red
Let yellow part be x m
The length of the black part was 3/4 of the length of the yellow part.
(3/4)x = 3x/4
7/4 +x+3x/4 = 7
7/4 +(x+3x/4) = 7
(x+3x/4) = 7 -7/4
(4x+3x)/4 =( 28-7)/4
cancel off 4
7x =21
x =3m yellow part
Black part = 3x/4 = 3*3/4 =9/4
2 1/4 m black part



7/4+3+9/4 =7












Answer by josgarithmetic(39630) About Me  (Show Source):
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He painted 1 3/4 of the pole red.
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That number needs the unit stated clearly. The pole alone is only 7 meters.


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pole measuring 7 m. He painted it red, yellow and black. He painted 1 3/4 METERS of the pole red. The length of the black part was 3/4 of the length of the yellow part. What was the length of the pole that was poured PAINTED black?
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Not the only way to assign a variable, but this is literally according to the description:
COLOR          AMOUNT_in_meters
black            %283%2F4%29y
red             1%263%2F4
yellow             y
SUM               7

highlight_green%283y%2F4%2B7%2F4%2By=7%29
-
3y%2B7%2B4y=28
7y%2B7=28
y%2B1=4
highlight_green%28y=3%29-----------the length of yellow part

The black part is %283%2F4%29%2A3=9%2F4=highlight%282%261%2F4%29 meters.


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Answer by Edwin McCravy(20064) About Me  (Show Source):
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Henry had a pole measuring 7 m. He painted it red, yellow and black. 

(1)  R+%2B+Y+%2B+B+=+7

He painted 1 3/4 of the pole red. 

1%263%2F4%2A7+=+R
(2)  7%2F4+=+R

The length of the black part was 3/4 of the length of the yellow part. 

(3) B=expr%283%2F4%29%2AY

What was the length of the pole that was cross%28poured%29 painted black?

Substitute (2) and (3) in (1)

R+%2B+Y+%2B+B+=+7 

7%2F4%2BY%2Bexpr%283%2F4%29%2AY=7

Multiply through by 4

7%2B4Y%2B3Y=28

7Y=21

Y=3

Substitute in (3)

B=expr%283%2F4%29%2Aexpr%283%29

B+=+9%2F4

B+=+2.25 meters

Edwin

Answer by greenestamps(13209) About Me  (Show Source):
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As you can see from the responses from the other tutors, there are many ways the problem can be set up for solving.

I note that in all three of the solutions you have received, the tutors use some form of the equation "black=(3/4)red". That fraction slows down the work of solving the problem.

A setup that seems easier to me is this:

yellow = 1 3/4 = 7/4
black = 3x
red = 4x

With those expressions for the lengths of black and red, it will always be true that the length of black is 3/4 the length of red. Now the equation that says the total length is 7m is easy:

3x%2B4x%2B7%2F4=7
7x=7-7%2F4=28%2F4-7%2F4=21%2F4
x=%2821%2F4%29%2F7=3%2F4

ANSWER: The length that was painted black is 3x = 9/4 m, or 2.25m