Jessamine wants to ride her bike at least 85 miles per week. She rides to and from school 5 days per week. Her house is 6.25 miles from her school. She rides an additional 2.5 miles for each trip, *t*, she makes around the park. Which inequality represents the situation?


Let's break down the information given to create the inequality step by step.

1. **Riding to and from school:**
   - Jessamine rides to and from school for 5 days.
   - One trip to school is 6.25 miles. Since it's a round trip (to and from), the total distance per day is \( 6.25 \times 2 = 12.5 \) miles.
   - In 5 days, the total distance she rides to and from school is \( 12.5 \times 5 = 62.5 \) miles.

2. **Riding in the park:**
   - She rides an additional 2.5 miles for each trip she makes around the park.
   - Let \( t \) represent the number of trips she makes around the park.
   - The total distance she rides in the park is \( 2.5t \) miles.

3. **Total miles:**
   - The total distance Jessamine rides in a week is the sum of the distance she rides to school and the distance she rides in the park:  
     \( 62.5 + 2.5t \).

4. **At least 85 miles:**
   - Jessamine wants to ride **at least 85 miles per week**. This means the total distance should be **greater than or equal to** 85 miles. Thus, the inequality becomes:
   \[
   62.5 + 2.5t \geq 85
   \]

Therefore, the inequality representing the situation is:
\[
62.5 + 2.5t \geq 85
\]

Would you like a step-by-step solution for solving the inequality?

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Here are 5 questions to expand the understanding:

1. How many park trips does Jessamine need to meet her goal exactly?
2. If Jessamine increases her park trip distance to 3 miles per trip, how does the inequality change?
3. How many total miles does Jessamine ride if she makes 4 trips around the park?
4. What happens if Jessamine only rides to and from school for 4 days a week?
5. If Jessamine wants to ride at least 100 miles a week, how would that change the inequality?

**Tip:** When solving word problems, always identify the variable and the relationships between given quantities.

Jessamine wants to ride her bike at least 85 miles per week. She rides to and from school 5 days per week. Her house is 6.25 miles from her school. She rides an additional 2.5 miles for each trip, t, she makes around the park. Which inequality represents the situation?

Solve the linear inequality representing Jessamine's weekly biking goal of at least 85 miles. This problem covers algebraic concepts like inequalities and linear equations, with a detailed breakdown of total distance calculations. Suitable for students in Grades 6-8.

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