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On a Saturday night, each of the rooms at a certain motel was rented

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On a Saturday night, each of the rooms at a certain motel was rented  [#permalink]

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New post 11 Nov 2015, 00:01
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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) $1,000
(D) $1,600
(E) $2,400

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Re: On a Saturday night, each of the rooms at a certain motel was rented  [#permalink]

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New post 11 Nov 2015, 00:34
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Let total rent the motel charge for all rooms =x
If 10 rooms that were rented for 60 $ had instead been rented for 40 $,
then total difference in prices = 20 $ * 10 = 200 $

Total rent the motel charged would have been reduced by 25 %
.25x = 200
=> x= 800
Answer B
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Re: On a Saturday night, each of the rooms at a certain motel was rented  [#permalink]

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New post 26 Mar 2020, 15:13
Bunuel wrote:
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) $1,000
(D) $1,600
(E) $2,400


Since the reduction in the original price will be (10*20$)= 200$

200$ is 25% of what amount?

800$

Hence Option B
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Re: On a Saturday night, each of the rooms at a certain motel was rented  [#permalink]

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New post 26 Mar 2020, 22:32
Bunuel wrote:
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) $1,000
(D) $1,600
(E) $2,400


Although this is a longer way but this is what had hit me when doing the question. Hope this helps some of you :)
So here it goes,

Let $40 rooms be 'a' in count
Let $60 rooms be 'b' in count
Let total rent be 'c'

Hence from first line of the prompt we can create this equation -
40a + 60 b = c - (1)

Now the second says, we removed 10 rooms from $60 lot and had put it out for $40 slots and rent was reduced by 25%, hence our (1) becomes as follows -
\(40 (a + 10) + 60 (b - 10) = \frac{3}{4}c\)
\(40a + 400 + 60b - 600 = \frac{3}{4}c\)
\(40a + 60b - 200 = \frac{3}{4}c\) - (2)

Using (1) and (2),

\(c - 200 = \frac{3}{4}c\)
\(\frac{1}{4}c = 200\)
c = 800

Hence B.


Even though it is a little time consuming but can be used when nothing strikes.
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Re: On a Saturday night, each of the rooms at a certain motel was rented  [#permalink]

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New post 29 Mar 2020, 03:57
Bunuel wrote:
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) $1,000
(D) $1,600
(E) $2,400



Solution:

If we let x = the number of $40 rooms and y = the number of $60 rooms, then the total rent for the motel is 40x + 60y. 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:

40(x + 10) + 60(y - 10) = (40x + 60y) * 3/4

160(x + 10) + 240(y - 10) = 120x + 180y

160x + 1600 + 240y - 2400 = 120x + 180y

40x + 60y = 800

Alternate Solution:

If 10 rooms were rented for $40 instead of $60, then the total rent would have been 10 * (60 - 40) = 10 * 20 = $200 less. We are given that this reduction corresponds to 25% of the total rent; thus, the total rent is 200/0.25 = $800.

Answer: B
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Re: On a Saturday night, each of the rooms at a certain motel was rented   [#permalink] 29 Mar 2020, 03:57

On a Saturday night, each of the rooms at a certain motel was rented

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