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

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by AAPL » Wed Feb 14, 2018 7:11 am
On 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 has 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

The OA is B.

I don't have clear this PS question.

I can say that the total rent for that night = $x.

If 10 rooms that were rented for 60 $ had instead been rented for 40 $, then the total difference in price will be = $20 * 10 = $200.

I stuck here. I appreciate if any expert explains it to me. Thank you so much.
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by DavidG@VeritasPrep » Wed Feb 14, 2018 11:00 am
AAPL wrote:On 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 has 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

The OA is B.

I don't have clear this PS question.

I can say that the total rent for that night = $x.

If 10 rooms that were rented for 60 $ had instead been rented for 40 $, then the total difference in price will be = $20 * 10 = $200.

I stuck here. I appreciate if any expert explains it to me. Thank you so much.
You're almost there. We know that this $200 reduction represents 25% of the original value. Algebraically, .25x = 200 --> x = 800. The answer is B
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by Scott@TargetTestPrep » Mon Feb 19, 2018 3:05 pm
DavidG@VeritasPrep wrote:
AAPL wrote:On 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 has 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
We can let T = total rent the motel actually charged. We also see that the hypothetical total rent was $200 less than the actual total rent since 10 of the rooms were charged $20 less each. Since this is a 25% decrease in total rent, we can say

T - 200 = 0.75T

0.25T = 200

(1/4)T = 200

T = 800

Answer: B

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