12000 people participated in a marathon in 2017. The number of participants increased by 10% in 2018, decreased by 15% in 2019 and increased by 5% in 2020.

(a)
Find the number of participants in 2020.
(b) Find the overall percentage change in the number of participants from 2017 to 2020.

Let's solve the problem step by step.

### (a) Finding the number of participants in 2020

We know the following:
- In 2017, there were 12,000 participants.
- The number of participants increased by 10% in 2018, decreased by 15% in 2019, and increased by 5% in 2020.

#### Step 1: Participants in 2018
- A 10% increase in 2018 means the number of participants in 2018 is:
\[
\text{Participants in 2018} = 12000 \times (1 + \frac{10}{100}) = 12000 \times 1.10 = 13200
\]

#### Step 2: Participants in 2019
- A 15% decrease in 2019 means the number of participants in 2019 is:
\[
\text{Participants in 2019} = 13200 \times (1 - \frac{15}{100}) = 13200 \times 0.85 = 11220
\]

#### Step 3: Participants in 2020
- A 5% increase in 2020 means the number of participants in 2020 is:
\[
\text{Participants in 2020} = 11220 \times (1 + \frac{5}{100}) = 11220 \times 1.05 = 11781
\]

So, the number of participants in 2020 is **11,781**.

---

### (b) Finding the overall percentage change from 2017 to 2020

The overall percentage change is calculated using the formula:
\[
\text{Percentage change} = \left( \frac{\text{Final value} - \text{Initial value}}{\text{Initial value}} \right) \times 100
\]
- The initial value (2017 participants) is 12,000.
- The final value (2020 participants) is 11,781.

\[
\text{Percentage change} = \left( \frac{11781 - 12000}{12000} \right) \times 100 = \left( \frac{-219}{12000} \right) \times 100 = -1.825\%
\]

So, the overall percentage change from 2017 to 2020 is approximately **-1.83%**, meaning there was a slight decrease in the number of participants.

---

### Summary:
- (a) The number of participants in 2020 is **11,781**.
- (b) The overall percentage change from 2017 to 2020 is **-1.83%** (a slight decrease).

Would you like more details or have any questions?

### 5 Related Questions:
1. What would the number of participants be in 2021 if there was a 7% increase from 2020?
2. How would the results change if the 2019 decrease was 20% instead of 15%?
3. What would be the total number of participants over the 4-year period from 2017 to 2020?
4. How do percentage changes compound over multiple years in general?
5. What would the number of participants be in 2020 if the initial value in 2017 was 15,000 instead?

### Tip:
When dealing with percentage changes over multiple periods, remember that the changes compound rather than simply adding or subtracting percentages directly.

12000 people participated in a marathon in 2017. The number of participants increased by 10% in 2018, decreased by 15% in 2019 and increased by 5% in 2020.

(a) Find the number of participants in 2020.
(b) Find the overall percentage change in the number of participants from 2017 to 2020.

Solve how the number of marathon participants changed from 2017 to 2020 with a step-by-step approach. Learn how to calculate the number of participants after a 10% increase, a 15% decrease, and a 5% increase. Understand the overall percentage change over four years. Ideal for Grades 8-10.

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