Question 12 Jeanette wants to raise \( \$ 3,200 \) in a marathon fundraiser. Her sponsers will donate \( \$ 35 \) for each (whole) kilometer she runs this summer. The minimum amount Jeanette will have to run to reach her goal of \( \$ 3,200 \) is kilometers. The solution is

To determine the minimum number of whole kilometers Jeanette needs to run to raise at least \$3,200, follow these steps: 1. **Understand the Relationship:** Jeanette raises \$35 for each kilometer she runs. If she runs \( k \) kilometers, the total amount raised (\( A \)) can be expressed as: \[ A = 35k \] 2. **Set Up the Inequality:** She wants to raise at least \$3,200, so: \[ 35k \geq 3200 \] 3. **Solve for \( k \):** Divide both sides of the inequality by 35 to find the minimum number of kilometers: \[ k \geq \frac{3200}{35} \] \[ k \geq 91.428... \] 4. **Determine the Minimum Whole Kilometer:** Since Jeanette can only run whole kilometers, she cannot run a fraction of a kilometer. Therefore, she needs to round up to the next whole number: \[ k \geq 92 \] 5. **Conclusion:** Jeanette must run **92 kilometers** to meet or exceed her fundraising goal of \$3,200. **Final Answer:** 92 kilometers