Problem Solving

Please help with this...

On a Saturday night, each of the rooms at a certain motel was rented for either $40 or $60. If 10 of the rooms that were rented for $60 had instead been rented for $40, then the total rent the motel charged for that night would have been reduced by 25 percent. What was the total rent the motel actually charged for that night?

(A) $600
(B) $800
(C) $1000
(D) $1600
(E) $2400

Let the actual rent motel charged for the night = x

Ten $60 rooms were rented for $40, so the rent didn't charge =
(60-40)x10 = 200

If all the rooms were to be charged for their actual price, rent collected
would have been = x+200

Total rent the motel charged was reduced by 25 percent, Or,
actual rent charged was 75% of the rent, if all rooms were rented for actual price.

x = (75/100)(x+200)
Or, x = 600. Choice A

Hey RM, my apologies for getting back so late but thanks so much.

answer should be 800..

it says IF the hotel charged then they would have lost 25%...

now if they charged $20 less for 10 rooms they lost 200$

therefore 25% of total = 200

total = 800

akay wrote:Please help with this...

On a Saturday night, each of the rooms at a certain motel was rented for either $40 or $60. If 10 of the rooms that were rented for $60 had instead been rented for $40, then the total rent the motel charged for that night would have been reduced by 25 percent. What was the total rent the motel actually charged for that night?

(A) $600
(B) $800
(C) $1000
(D) $1600
(E) $2400

I am agree with Hopefully. The explanation is like -
Suppose,
60$ room = x; 40$ room = y
That night's income = 60x+40y
But according to the condition,
[{60x + 40y - {(60(x - 10) + 40(y + 10)}]/(60x + 40y)}] * 100 = 25
So 60x + 40y = 800

Wow, lots of debate on this one. I am in the camp for the answer being $800. What is the OA?

Let rent collected by hotel on every day basis be x

so rent collected that night would be x - 200 (20 * 10 rooms)

so Q say this 25 % less than normal rent i.e 75 % of normal rent

so x -200 = (75/100) * x

solving we get x =800

Q ask rent collected that night i.e x-200 =600

So and should be 600 A

akay wrote:Please help with this...

On a Saturday night, each of the rooms at a certain motel was rented for either $40 or $60. If 10 of the rooms that were rented for $60 had instead been rented for $40, then the total rent the motel charged for that night would have been reduced by 25 percent. What was the total rent the motel actually charged for that night?

(A) $600
(B) $800
(C) $1000
(D) $1600
(E) $2400

quite a lot of discussion over here .. seems like a pretty straightforward question...

Let the total number of rooms charged at 40$ be "a" and that charged at 60$ be "b"..

.. So the total rent for that night = 40*a + 60* b ..

..Now according to the condition given the number of rooms charged at 40$ is " a+10" and that charged at 60$ is "b-10" ..

.. so the total rent in this case = 40*(a+10)+60*(b-10) .. now we know that this value is 75% of the original value ..

..So, we have 40*a+60*b=3/4(40*(a+10)+60*(b-10))..

.. 3(40*a+60*b)=4( 40*a+60*b +400-600)..

solving the 2 sides and we get 40a+60b= 800 .. which is the rent for that night ..

samirpandeyit62 wrote:Let rent collected by hotel on every day basis be x

so rent collected that night would be x - 200 (20 * 10 rooms)

so Q say this 25 % less than normal rent i.e 75 % of normal rent

so x -200 = (75/100) * x

solving we get x =800

actually the answer should end over here .

samirpandeyit62 wrote: Q ask rent collected that night i.e x-200 =600

So and should be 600 A

This is just the "if" part not what actually happened ...

Yes gabriel did not read that if part properly, thanks for correcting.