The Nursing Home Problem. Suppose that the cost of nursing homes (per year) for the following states is as follows for 2004:
Alaska: $165,000
Connecticut $95,000
Hawaii $85,000
New York $110,000
If each state had a $10,000 cost increase since 1994, rank order the states in terms of their percent increase of costs (least to greatest) without actually doing the calculations. Explain how you established your ranking.
This is a thought question. Think about it.
percent = amount of increase/cost.
The amount of increase is constant at $10,000; therefore, the smallest cost per year will be the largest increase. Follow that reasoning to complete the ranking.
Is it Alaska, New York, Connecticut, and Hawaii?
Why not just take you calculator and calculate them to see if you are right. But I would give you a good grade for your answer.
To rank the states in terms of their percent increase of costs without actually doing the calculations, you can follow these steps:
1. Identify the original cost for each state in 1994 by subtracting the $10,000 increase from the 2004 cost:
- Alaska: $165,000 - $10,000 = $155,000
- Connecticut: $95,000 - $10,000 = $85,000
- Hawaii: $85,000 - $10,000 = $75,000
- New York: $110,000 - $10,000 = $100,000
2. Calculate the difference between the original cost in 1994 and the 2004 cost for each state:
- Alaska: $165,000 - $155,000 = $10,000
- Connecticut: $95,000 - $85,000 = $10,000
- Hawaii: $85,000 - $75,000 = $10,000
- New York: $110,000 - $100,000 = $10,000
3. Since the cost increase for all states is the same ($10,000), the percent increase in costs will be the same for all states. Therefore, all the states will have the same rank in terms of percent increase.
Therefore, the ranking order of the states in terms of their percent increase of costs, from least to greatest, is:
1. Alaska
2. Connecticut
3. Hawaii
4. New York