represent any 5 daily life situations in the form of linear equation and solve them

You go for a run and track your distance covered each day. On Day 1, you run 5 kilometers. Every day thereafter, you increase your distance by 0.5 kilometers.

**Linear Equation:**

Let $ D $ represent the distance covered in kilometers after $ n $ days.

\[ D = 5 + 0.5n \]

**Solution:**

- For Day 1 ($ n = 1 $): $ D = 5 + 0.5 \times 1 = 5.5 $ kilometers

- For Day 2 ($ n = 2 $): $ D = 5 + 0.5 \times 2 = 6 $ kilometers

- For Day 3 ($ n = 3 $): $ D = 5 + 0.5 \times 3 = 6.5 $ kilometers

- and so on.

**2. Situation:**

You are saving money each month for a vacation. In the first month, you save $200, and each subsequent month you increase your savings by $50.

**Linear Equation:**

Let $ S $ represent the amount of money saved after $ n $ months.

\[ S = 200 + 50n \]

**Solution:**

- After 1 month ($ n = 1 $): $ S = 200 + 50 \times 1 = 250 $ dollars

- After 2 months ($ n = 2 $): $ S = 200 + 50 \times 2 = 300 $ dollars

- After 3 months ($ n = 3 $): $ S = 200 + 50 \times 3 = 350 $ dollars

- and so on.

**3. Situation:**

You are driving and notice your fuel gauge decreases linearly as you drive. When the tank is full, the gauge shows 100%. After driving 300 kilometers, the gauge shows 75%.

**Linear Equation:**

Let $ F $ represent the fuel gauge percentage after driving $ d $ kilometers.

\[ F = 100 - \frac{25}{300} d \]

**Solution:**

- After driving 0 kilometers ($ d = 0 $): $ F = 100 $% (tank is full)

- After driving 300 kilometers ($ d = 300 $): $ F = 100 - \frac{25}{300} \times 300 = 75 $%

**4