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# Algebra/Algebra

Question
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.

Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment You made this answer very clear - thanks.

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Algebra

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#### Scott A Wilson

##### Expertise

Any algebraic question you've got. That includes question that are linear, quadratic, exponential, etc.

##### Experience

I have solved story problems, linear equations, parabolic equations. I have also solved some 3rd order equations and equations with multiple variables.

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Documents at Boeing in assistance on the manufacturiing floor.

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MS at math OSU in mathematics at OSU, 1986. BS at OSU in mathematical sciences (math, statistics, computer science), 1984.

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Both my BS and MS degrees were given with honors.

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