The news media is reporting a 24% increase in hotel costs in 2021 over 2020.

a) If a room cost $75 a night to rent in 2020, what would the expected cost be in 2021?
     
 
Select an answer


b) If a room cost $150 in 2021, what would it have cost if rented last year?
     
   
Select an answer


Let's solve both parts of the problem using percentage increase and decrease formulas.

### Part (a): 
**If a room cost $75 a night to rent in 2020, what would the expected cost be in 2021 given a 24% increase?**

To calculate the cost after a percentage increase, use the formula:
\[
\text{New Price} = \text{Original Price} \times (1 + \text{Percentage Increase as a Decimal})
\]

Given:
- Original Price = $75
- Percentage Increase = 24% = 0.24

The expected cost in 2021:
\[
\text{New Price} = 75 \times (1 + 0.24) = 75 \times 1.24 = 93
\]

**Answer:** The expected cost in 2021 would be **$93**.

### Part (b):
**If a room cost $150 in 2021, what would it have cost if rented last year (2020)?**

Here, you need to reverse the percentage increase. The formula for the original price before a percentage increase is:
\[
\text{Original Price} = \frac{\text{New Price}}{1 + \text{Percentage Increase as a Decimal}}
\]

Given:
- New Price = $150
- Percentage Increase = 24% = 0.24

The cost in 2020:
\[
\text{Original Price} = \frac{150}{1.24} \approx 120.97
\]

**Answer:** The cost in 2020 would have been approximately **$120.97**.

Would you like further details or have any questions?

Here are 5 relative questions:
1. How would you calculate the price in 2022 with another 10% increase on the 2021 price?
2. How do you handle decreases in price using percentages?
3. If the price had increased by 50% instead of 24%, what would the 2021 price be?
4. How do you calculate the percentage increase if you know both the 2020 and 2021 prices?
5. How would the formula change if the percentage increase was compounded monthly instead of annually?

**Tip:** When calculating percentage increases or decreases, it's often useful to express the percentage as a decimal and adjust the original value accordingly.

Learn how to calculate expected hotel room costs in 2021 based on a 24% increase over 2020 prices, and reverse the calculation to find 2020 costs given 2021 prices. Understand the formulas and methods for percentage increase and decrease in practical scenarios.

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