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

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Math Expert
Joined: 02 Sep 2009
Posts: 50711
In a certain town, the ratio of the number of rented residences to the  [#permalink]

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21 Dec 2017, 20:31
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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

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Joined: 10 Apr 2013
Posts: 13
Re: In a certain town, the ratio of the number of rented residences to the  [#permalink]

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21 Dec 2017, 20:38
Owner=200 and rent=350, total 550

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Intern
Joined: 02 Apr 2017
Posts: 11
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22 Dec 2017, 07:57
Given that R/O = 7/4

R /R-150 = 7/4

4R = 7R - 1050

R = 350
O = 200

Hence, R + O = 550
Manager
Joined: 24 Nov 2016
Posts: 152
Re: In a certain town, the ratio of the number of rented residences to the  [#permalink]

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23 Dec 2017, 07:25
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.
Math Expert
Joined: 02 Aug 2009
Posts: 7039
In a certain town, the ratio of the number of rented residences to the  [#permalink]

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23 Dec 2017, 07:32
1
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 &nbs [#permalink] 23 Dec 2017, 07:32
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