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# In a certain town, the ratio of the number of rented residen

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Senior Manager
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In a certain town, the ratio of the number of rented residen [#permalink]  20 Nov 2017, 10:28
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Question Stats:

71% (00:58) correct 28% (01:22) wrong based on 7 sessions
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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Re: In a certain town, the ratio of the number of rented residen [#permalink]  01 Dec 2017, 22:42
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

Here

$$\frac{Rent}{owned} = \frac{R}{O} = \frac{7}{4}$$ (Let R= rent and O = owned)

but Rent = owned + 150

therefore the fraction can be written as = $$\frac{{O+150}}{0} = \frac{7}{4}$$

or O = 200

substituting the value of O we get R = 350.

therefore total = rent + owned = 550
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Manager
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Re: In a certain town, the ratio of the number of rented residen [#permalink]  25 May 2018, 22:08
pranab01 wrote:
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

Here

$$\frac{Rent}{owned} = \frac{R}{O} = \frac{7}{4}$$ (Let R= rent and O = owned)
but Rent = owned + 150

therefore the fraction can be written as = $$\frac{{O+150}}{0} = \frac{7}{4}$$

or O = 200

substituting the value of O we get R = 350.

therefore total = rent + owned = 550

how did you come up with this equation.
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Re: In a certain town, the ratio of the number of rented residen [#permalink]  26 May 2018, 00:47
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Expert's post
I am assuming you have understood how the equation are obatined

$$\frac{R}{O} = \frac{7}{4}$$

and $$R=O+150$$

Substitiing R in the first equation...

$$\frac{O+150}{O} = \frac{7}{4}$$

Solve for O $$(O+150) \times 4 = 7O$$ or $$3O=150 \times 4$$ or $$O=200$$.

So we can find the value of R which is O+150 = 350.

So total number of houses is R+O=350+200=550.
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Re: In a certain town, the ratio of the number of rented residen   [#permalink] 26 May 2018, 00:47
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