confused one

[hakyology]

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 totla rent the motel actually charged for that night?

A)$600
B)$800
C)$1,000
D)$1,600
E)$2,400


Please explain.

The answer is B.

I got $850 where it is not there among the answer choices.

[sethids]

x = No. of rooms rented for $40
y = No. of rooms rented for $60

We need to find the value of 40x + 60y which is the total value of the rooms rented on the particular night.

deducing the equation from given information:
(40x + 60y)*3/4 = 40(x + 10) + 60(y - 10)
=> 120x + 180y = 160x + 1600 + 240y - 2400

simplifying on both sides we get:
40x + 60y = 800.

Hence B is the answer.

[kanak]

Yes. The ans is B. Here's how:

Let there be x other rooms apart from the 10 rooms.

10 rooms @ $60 = $600
Rest of the rooms (i.e., x) @ $40 = 40x

600 + 40x is the cost.

If 10 rooms had $40 as rent = $400
Rest of the rooms = 40x

400 + 40x is the alternative cost.

600 + 40x = T
400 + 40x = (3/4) T

solve for T and you'll get
T = 800.

[hakyology]

hm...i do not get that. could you explain further? thanks.

[Robertogmat]

hm...i do not get that. could you explain further? thanks.

another way to solve it:

If the hotel had rented the 10 rooms for Usd 40 instead of usd 60, it would have lost USd 20 * 10 rooms = Usd200

Usd 200 corresponds to the reduction of 25%.
therefore:

0.25x=200
x=800

[amitdgr]

To find => total cost = x

"If 10 of the rooms that were rented for $60 had instead been rented for $40"

i.e. instead of charging 60*10 for ten rooms, if they had charged 40*10

"then the total rent the motel charged for that night would have been reduced by 25 percent"

i.e. the rent lost = (60*10) - (40*10) = 200 is actually 25% of x

put into equation , 200 = 0.25x

=> x= USD 800

HTH

Amit

[amitdgr]

I got $850 where it is not there among the answer choices.

Can you explain the method you tried ? So that we can find out where you went wrong. Might help us to avoid any such mistake in the future.


Amit

[AleksandrM]

Hey, how come you can't solve this problem using the following equation?

(40y + 600) - (40y + 400)/ 40y + 600 = .25

You would end up with y = 35

Then you had a rent of 40(35) + 600 = 2000

But instead you had 40(35) + 400 = 1800

[AleksandrM]

Never mind. I see my mistake. Instead of making the first figure R for total rent and second 3/4R for the reduced rent, I made them both R.