Input values into Z ranging from 100-300 in multiples of 20 then solve for p/z. Afterwards, show the percentage increase between the previous values of p/z.

p = ((.5*z)-9)*122.5)) then add 2025 to the final value to get P

Let's solve the problem with the corrected formula for \( p \).

Given:
- \( z = \text{Bullets fired} \) (values from 100 to 300 in multiples of 20)

The formula for total damage \( p \) is:
\[
p = \left( (0.5 \cdot z - 9) \times 122.5 \right) + 2025
\]

We will calculate \( \frac{p}{z} \) for \( z \) ranging from 100 to 300 in multiples of 20, and then calculate the percentage increase between successive values.

### Calculations

#### For \( z = 100 \):
\[
p = \left( (0.5 \cdot 100 - 9) \times 122.5 \right) + 2025
\]
\[
p = \left( (50 - 9) \times 122.5 \right) + 2025
\]
\[
p = (41 \times 122.5) + 2025
\]
\[
p = 5022.5 + 2025
\]
\[
p = 7047.5
\]
\[
\frac{p}{z} = \frac{7047.5}{100} = 70.475
\]

#### For \( z = 120 \):
\[
p = \left( (0.5 \cdot 120 - 9) \times 122.5 \right) + 2025
\]
\[
p = \left( (60 - 9) \times 122.5 \right) + 2025
\]
\[
p = (51 \times 122.5) + 2025
\]
\[
p = 6247.5 + 2025
\]
\[
p = 8272.5
\]
\[
\frac{p}{z} = \frac{8272.5}{120} \approx 68.9375
\]

#### For \( z = 140 \):
\[
p = \left( (0.5 \cdot 140 - 9) \times 122.5 \right) + 2025
\]
\[
p = \left( (70 - 9) \times 122.5 \right) + 2025
\]
\[
p = (61 \times 122.5) + 2025
\]
\[
p = 7472.5 + 2025
\]
\[
p = 9497.5
\]
\[
\frac{p}{z} = \frac{9497.5}{140} \approx 67.8375
\]

#### For \( z = 160 \):
\[
p = \left( (0.5 \cdot 160 - 9) \times 122.5 \right) + 2025
\]
\[
p = \left( (80 - 9) \times 122.5 \right) + 2025
\]
\[
p = (71 \times 122.5) + 2025
\]
\[
p = 8697.5 + 2025
\]
\[
p = 10722.5
\]
\[
\frac{p}{z} = \frac{10722.5}{160} \approx 67.015625
\]

#### For \( z = 180 \):
\[
p = \left( (0.5 \cdot 180 - 9) \times 122.5 \right) + 2025
\]
\[
p = \left( (90 - 9) \times 122.5 \right) + 2025
\]
\[
p = (81 \times 122.5) + 2025
\]
\[
p = 9922.5 + 2025
\]
\[
p = 11947.5
\]
\[
\frac{p}{z} = \frac{11947.5}{180} \approx 66.375
\]

#### For \( z = 200 \):
\[
p = \left( (0.5 \cdot 200 - 9) \times 122.5 \right) + 2025
\]
\[
p = \left( (100 - 9) \times 122.5 \right) + 2025
\]
\[
p = (91 \times 122.5) + 2025
\]
\[
p = 11147.5 + 2025
\]
\[
p = 13172.5
\]
\[
\frac{p}{z} = \frac{13172.5}{200

Explore how to solve linear equations and calculate percentage increase with detailed examples. This problem involves using the formula p = (0.5 * z - 9) * 122.5 + 2025 for different values of z ranging from 100 to 300 in multiples of 20. Suitable for advanced high school students interested in algebra and applied mathematics.

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