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In a certain town, the ratio of the number of rented residences to the

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In a certain town, the ratio of the number of rented residences to the [#permalink]

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New post 21 Dec 2017, 21:31
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In a certain town, the ratio of the number of rented residences to the number of owned residences is 7:4. Those are the only two kinds of residences in this town. If there are 150 more rented than owned residences in this town, what is the total number of residences in the town?

A. 200
B. 350
C. 550
D. 700
E. 1100
[Reveal] Spoiler: OA

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Re: In a certain town, the ratio of the number of rented residences to the [#permalink]

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New post 21 Dec 2017, 21:38
Owner=200 and rent=350, total 550

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Re: In a certain town, the ratio of the number of rented residences to the [#permalink]

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New post 22 Dec 2017, 08:57
Given that R/O = 7/4

R /R-150 = 7/4

4R = 7R - 1050

R = 350
O = 200

Hence, R + O = 550
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Re: In a certain town, the ratio of the number of rented residences to the [#permalink]

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New post 23 Dec 2017, 08:25
Bunuel wrote:
In a certain town, the ratio of the number of rented residences to the number of owned residences is 7:4. Those are the only two kinds of residences in this town. If there are 150 more rented than owned residences in this town, what is the total number of residences in the town?

A. 200
B. 350
C. 550
D. 700
E. 1100


\(Rented = r\); and \(Owned = w\)

\(\frac{r}{w}=\frac{7}{4}\) and \(r=w + 150\);

\(\frac{r}{w}=\frac{(w + 150)}{w}=\frac{7}{4};(w + 150)*4=7w;4w+600=7w;600=3w;w=200\)

\(r = w + 150;r = (200)+150 = 350\)

\(Total = w+r=(350)+(200)=550\)

(C) is the answer.
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In a certain town, the ratio of the number of rented residences to the [#permalink]

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New post 23 Dec 2017, 08:32
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Bunuel wrote:
In a certain town, the ratio of the number of rented residences to the number of owned residences is 7:4. Those are the only two kinds of residences in this town. If there are 150 more rented than owned residences in this town, what is the total number of residences in the town?

A. 200
B. 350
C. 550
D. 700
E. 1100


May be a slightly easier and faster approach..

Ratio 7:4, so numbers can be 7x and 4x.. total = 11x
your answer in form 11x means a MULTIPLE of 11... ONLY C and E

difference = \(7x-4x=3x=150.....x=\frac{150}{3}=50\)..
so total = \(11x=11*50=550\)

C
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In a certain town, the ratio of the number of rented residences to the   [#permalink] 23 Dec 2017, 08:32
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