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.

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

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

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

your approach is nice.
Just a syntax mistake it should be 7x-150=4x

Thank you! Noted on the syntax.

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

Thank you Chetan2u!

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