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# A painter has painted one-third of a rect- angular wall that is ten

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Math Expert
Joined: 02 Sep 2009
Posts: 52294
A painter has painted one-third of a rect- angular wall that is ten  [#permalink]

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06 Feb 2018, 02:02
00:00

Difficulty:

35% (medium)

Question Stats:

73% (02:25) correct 27% (02:20) wrong based on 51 sessions

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A painter has painted one-third of a rectangular wall that is ten feet high. When she has painted another 75 square feet of wall, she will be three-quarters finished with the job. What is the length (the horizontal dimension) of the wall?

(A) 18 feet

(B) 12 feet

(C) 10 feet

(D) 9 feet

(E) 6 feet

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Re: A painter has painted one-third of a rect- angular wall that is ten  [#permalink]

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06 Feb 2018, 02:10
A

We have ((3/4-1/3)*10)*w=75 sqft

Solving we get w=18 ft

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Re: A painter has painted one-third of a rect- angular wall that is ten  [#permalink]

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06 Feb 2018, 05:04
Bunuel wrote:
A painter has painted one-third of a rectangular wall that is ten feet high. When she has painted another 75 square feet of wall, she will be three-quarters finished with the job. What is the length (the horizontal dimension) of the wall?

(A) 18 feet

(B) 12 feet

(C) 10 feet

(D) 9 feet

(E) 6 feet

An additional approach to the one given above, which is especially useful if we tend to be confused by word problems, is to just use the answers.
This is an Alternative method.

Let's say the answer is the median - (C).
If the length is 10 feet then the dimensions are 10 by 10 and the area is 100 square feet.
So 1/3 of 100 = 33 square feet have been painted and there are only 67 left.
This is impossible as we know that an additional 75 square feet can be painted.
We need a larger length so (C) is eliminated, along with the smaller (D) and (E).

Repeating for (B) gives a total area of 120 meaning that 40 have been painted.
If another 75 were painted then a total of 40 + 75 = 115 would be painted, more than 3/4.
(B) is eliminated.

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Re: A painter has painted one-third of a rect- angular wall that is ten  [#permalink]

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08 Feb 2018, 15:42
Bunuel wrote:
A painter has painted one-third of a rectangular wall that is ten feet high. When she has painted another 75 square feet of wall, she will be three-quarters finished with the job. What is the length (the horizontal dimension) of the wall?

(A) 18 feet

(B) 12 feet

(C) 10 feet

(D) 9 feet

(E) 6 feet

We can let n = the total area of the wall and create the equation:

n/3 + 75 = 3n/4

Multiplying by 12, we have:

4n + 900 = 9n

900 = 5n

180 = n

So the length is 180/10 = 18 feet.

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Re: A painter has painted one-third of a rect- angular wall that is ten &nbs [#permalink] 08 Feb 2018, 15:42
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