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In a certain apartment building, there are one-bedroom and two-bedroom

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In a certain apartment building, there are one-bedroom and two-bedroom [#permalink] New post   16 Sep 2021, 09:41
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In a certain apartment building, there are one-bedroom and two-bedroom apartments. The rental prices of the apartment depend on a number of factors, but on average, two-bedroom apartments have higher rental prices than do one-bedroom apartments. Let R be the average rental price for all apartments in the building. If R is $5,600 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is $10,400 higher that R, then what percentage of apartments in the building are two-bedroom apartments?

(A) 26%
(B) 35%
(C) 39%
(D) 42%
(E) 52%
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Re: In a certain apartment building, there are one-bedroom and two-bedroom [#permalink] New post   16 Sep 2021, 19:40
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We have one bedroom & two-bedroom apartment.
Let's say the no of one bedroom apt \(= x\) & two bedroom apt \(= y\)
& avg of one bedroom apt \(= a\) & avg of two bedroom \(= b\)

R is the average rental price for all apartments in the building. If R is $5,600 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is $10,400 higher than R

\(R = a + 5600\) & \(b = R + 10400\)

Average Rent \(R = \frac{xa + yb}{x + y}\)

\(R = \frac{x(R - 5600) + y(R + 10400)}{x + y}\)

\(Rx+Ry = Rx - 5600x + Ry + 10400y\)

\(5600x = 10400y\)

\(\frac{y}{x} = \frac{7}{13}\)

2 bedroom apt \(= \frac{7}{20} = 35\)%

Answer B
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Re: In a certain apartment building, there are one-bedroom and two-bedroom [#permalink] New post   21 May 2024, 00:55
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Re: In a certain apartment building, there are one-bedroom and two-bedroom [#permalink]
21 May 2024, 00:55
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