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

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Bunuel
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In a certain town, the ratio of the number of rented residen [#permalink] New post   20 Nov 2017, 10:28
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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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Re: In a certain town, the ratio of the number of rented residen [#permalink] New post   01 Dec 2017, 22:42
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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





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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Re: In a certain town, the ratio of the number of rented residen [#permalink] New post   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] New post   26 May 2018, 00:47
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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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In a certain town, the ratio of the number of rented residen [#permalink] New post   27 Oct 2018, 08:58
Expert Reply
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] New post   31 Oct 2018, 22:44
1
let r=rented residence
let x=owned residence

From the question we can get two eqn
(i) 4r = 7x derived from the ratio
(ii) r =x+150

multiplying option (ii) by 4 we get,
4r = 4x + 600
replacing the value of (ii) in (i) we get,
4x + 600 = 7x
solving for x we get, x = 200

from eqn (ii) before modification we had,
r = x+150
or, r = 200 +150 = 350
therefore, total houses = 350+200 = 550
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Re: In a certain town, the ratio of the number of rented residen [#permalink] New post   31 Oct 2018, 23:47
Hi,

I used a different method & got the answer right..but am not sure if this is the right way to do it. Please feel free to mention if it's incorrect.

Rented : Owned = 7x:4x

150 more rented residences - 7x + 150 = 4x.
I solved for 'x' x = 50.

Rented : Owned =7x:4x
= 7(50)+ 4(50)
= 350 + 200
= 550
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Re: In a certain town, the ratio of the number of rented residen [#permalink] New post   01 Nov 2018, 04:05
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your approach is nice.
Just a syntax mistake it should be 7x-150=4x
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Re: In a certain town, the ratio of the number of rented residen [#permalink] New post   01 Nov 2018, 08:45
amorphous wrote:
your approach is nice.
Just a syntax mistake it should be 7x-150=4x



Thank you! Noted on the syntax.
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Re: In a certain town, the ratio of the number of rented residen [#permalink] New post   01 Nov 2018, 08:50
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anudec4 wrote:
Hi,

I used a different method & got the answer right..but am not sure if this is the right way to do it. Please feel free to mention if it's incorrect.

Rented : Owned = 7x:4x

150 more rented residences - 7x + 150 = 4x.
I solved for 'x' x = 50.

Rented : Owned =7x:4x
= 7(50)+ 4(50)
= 350 + 200
= 550


Hi..
that is a very logical and short method..
if difference in the two quantities is 150, 7x-4x=150...x=50
total = 7x+4x=11x=11*50=550
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Re: In a certain town, the ratio of the number of rented residen [#permalink] New post   02 Nov 2018, 02:52
Thank you Chetan2u!
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Re: In a certain town, the ratio of the number of rented residen [#permalink] New post   19 Jan 2021, 05:43
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