A company's revenue increased by 20% from 2019 to 2020. In 2021, the revenue decreased by 25%, bringing it down to $180,000. What was the revenue in 2019?A) $150,000

B) $160,000

C) $200,000

D) $225,000

E) $240,000

To find the revenue in 2019, let's work backwards from the information given about 2021 and 2020.

### Step-by-step Solution:

1. **Revenue in 2021**: It's given that the revenue in 2021 is $180,000.

2. **Revenue decrease from 2020 to 2021**: The revenue decreased by 25% in 2021.
   
   - If the revenue in 2020 is $ R_{2020} $, then a 25% decrease means:
   
   \[
   R_{2021} = R_{2020} \times (1 - 0.25) = R_{2020} \times 0.75
   \]

3. **Set up the equation for 2020 revenue**:

   \[
   180,000 = R_{2020} \times 0.75
   \]

4. **Solve for $ R_{2020} $**:

   \[
   R_{2020} = \frac{180,000}{0.75} = 240,000
   \]

5. **Revenue increase from 2019 to 2020**: The revenue increased by 20% from 2019 to 2020.
   
   - If the revenue in 2019 is $ R_{2019} $, then a 20% increase means:
   
   \[
   R_{2020} = R_{2019} \times (1 + 0.20) = R_{2019} \times 1.20
   \]

6. **Set up the equation for 2019 revenue**:

   \[
   240,000 = R_{2019} \times 1.20
   \]

7. **Solve for $ R_{2019} $**:

   \[
   R_{2019} = \frac{240,000}{1.20} = 200,000
   \]

### Conclusion:

The revenue in 2019 was **$200,000**.

So, the correct answer is **C) $200,000**.

---

Would you like more details on any step or have any questions? Here are some related questions for further practice:

1. If the company's revenue decreased by 30% from 2021 to 2022, what would be the revenue in 2022?
2. If instead of a 25% decrease, the revenue in 2021 had only decreased by 10%, what would the revenue in 2019 have been?
3. How much revenue would the company need to make in 2023 to achieve a 10% increase from its 2019 revenue?
4. If the company’s revenue increased by 15% in 2022 from its 2021 value, what would be the revenue in 2022?
5. If the revenue in 2020 was double the revenue in 2019, what would the 2019 revenue be?

**Tip:** When solving percentage problems involving increases and decreases, it’s often helpful to convert the percentage changes into decimal multipliers. This makes setting up equations and solving for unknowns straightforward.

Learn how to calculate revenue changes using percentage increase and decrease. Solve a problem where a company's revenue increased by 20% from 2019 to 2020, then decreased by 25% in 2021. Find the revenue in 2019 with a detailed step-by-step solution.

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