To calculate the percentage damage increase in damage per bullet. Plug in values 100 and 300 in for y and calculate the percent increase in comparison to an initial base of 100. We will use the given variables:

y= bullets fired
x = 145
z = 100
Total damage = [(y-18)*122.5]+2025

Total damage/y = Damage per bullet

To calculate the percentage damage increase per bullet when the number of bullets fired \( y \) changes from 100 to 300, we need to follow these steps:

1. **Calculate the total damage for \( y = 100 \):**

   \[
   \text{Total damage} = [(y - 18) \times 122.5] + 2025
   \]

   Plugging in \( y = 100 \):

   \[
   \text{Total damage}_{100} = [(100 - 18) \times 122.5] + 2025
   \]

   \[
   \text{Total damage}_{100} = [82 \times 122.5] + 2025
   \]

   \[
   \text{Total damage}_{100} = 10045 + 2025
   \]

   \[
   \text{Total damage}_{100} = 12070
   \]

2. **Calculate the damage per bullet for \( y = 100 \):**

   \[
   \text{Damage per bullet}_{100} = \frac{\text{Total damage}_{100}}{100}
   \]

   \[
   \text{Damage per bullet}_{100} = \frac{12070}{100}
   \]

   \[
   \text{Damage per bullet}_{100} = 120.7
   \]

3. **Calculate the total damage for \( y = 300 \):**

   \[
   \text{Total damage}_{300} = [(300 - 18) \times 122.5] + 2025
   \]

   \[
   \text{Total damage}_{300} = [282 \times 122.5] + 2025
   \]

   \[
   \text{Total damage}_{300} = 34545 + 2025
   \]

   \[
   \text{Total damage}_{300} = 36570
   \]

4. **Calculate the damage per bullet for \( y = 300 \):**

   \[
   \text{Damage per bullet}_{300} = \frac{\text{Total damage}_{300}}{300}
   \]

   \[
   \text{Damage per bullet}_{300} = \frac{36570}{300}
   \]

   \[
   \text{Damage per bullet}_{300} = 121.9
   \]

5. **Calculate the percentage increase in damage per bullet:**

   \[
   \text{Percentage increase} = \left( \frac{\text{Damage per bullet}_{300} - \text{Damage per bullet}_{100}}{\text{Damage per bullet}_{100}} \right) \times 100
   \]

   \[
   \text{Percentage increase} = \left( \frac{121.9 - 120.7}{120.7} \right) \times 100
   \]

   \[
   \text{Percentage increase} = \left( \frac{1.2}{120.7} \right) \times 100
   \]

   \[
   \text{Percentage increase} \approx 0.994\%
   \]

The percentage increase in damage per bullet when the number of bullets fired changes from 100 to 300 is approximately \( 0.994\% \).

Do you want more details or have any questions?

Here are some related questions for further practice:
1. How would the percentage increase change if the initial number of bullets fired was different?
2. What is the total damage for 200 bullets fired?
3. How does the formula change if the base damage (2025) increases?
4. What if the damage per bullet (\( 122.5 \)) was altered?
5. How does the damage per bullet change if only 50 bullets are fired?
6. Calculate the total damage for 400 bullets fired.
7. What is the percentage increase in damage per bullet if the final number of bullets fired is 500?
8. How does the total damage change if the number of bullets fired is halved?

**Tip:** Understanding how to break down a problem step-by-step can help simplify complex calculations and improve accuracy.

Learn how to calculate the percentage increase in damage per bullet when the number of bullets fired changes from 100 to 300. This problem involves arithmetic calculations and percentage increase formulas. Suitable for students in Grades 7-9.

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