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A nursing home has two daily room rates, $320 for semi & %340 for private rooms. There were 1000 chargable days & total revenue was $328,000. How do you find out how many days were for semi & how many were private? (In this case I know thre answer is 600 semi & 400 private - but I would like to see the steps to get the answer since I will have to do this each month) My phone is , ext if you have any qustions. Thanks!

If the amount charged is $320 and $340.

If all rooms were at $320, the revenue would have been $320,000.

If all rooms were at $340, the revenue would have been $340,000.

Since the revenue is $328,000, that is 328K - 320K = 8K over the low and

340K - 328K = 12K under the high.

The total difference is 8K + 12K = 20K.

Since 8 is 2/5 or 20 and 12 is 3/5 or 20, that means that 3/5 of the rooms were at the lower rate. Out of 1000 rooms, 3/5 is 600, so 600 were at the lower rate.

Another way to view this problem is to think if we had only rented the cheap rooms, we would have gotten only $320,000 in 1,000 days. Since we got an extra $8,000, and the difference in rental price is $20, that is 8,000/20 = 400 rooms at the higher price. That leaves a total of

1000-400=600 rooms at the regular price.

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