To determine which options satisfy the inequality [tex]\( y \geq 0.6x + 1.25 \)[/tex], let's analyze each scenario step by step:
### Option a: Having 3.2 liters of water for 3 hours of hiking
1. Calculate the required amount of water for 3 hours:
[tex]\[
y \geq 0.6 \cdot 3 + 1.25
\][/tex]
2. Perform the multiplication:
[tex]\[
0.6 \cdot 3 = 1.8
\][/tex]
3. Add the reserve amount:
[tex]\[
y \geq 1.8 + 1.25 \quad \rightarrow \quad y \geq 3.05
\][/tex]
4. Compare the given amount of water (3.2 liters) to the required amount (3.05 liters):
[tex]\[
3.2 \geq 3.05 \quad \text{(True)}
\][/tex]
Thus, option (a) satisfies the inequality.
### Option b: Having 2 liters of water for 2.5 hours of hiking
1. Calculate the required amount of water for 2.5 hours:
[tex]\[
y \geq 0.6 \cdot 2.5 + 1.25
\][/tex]
2. Perform the multiplication:
[tex]\[
0.6 \cdot 2.5 = 1.5
\][/tex]
3. Add the reserve amount:
[tex]\[
y \geq 1.5 + 1.25 \quad \rightarrow \quad y \geq 2.75
\][/tex]
4. Compare the given amount of water (2 liters) to the required amount (2.75 liters):
[tex]\[
2 \geq 2.75 \quad \text{(False)}
\][/tex]
Thus, option (b) does not satisfy the inequality.
### Option c: Having 3 liters of water for 3.5 hours of hiking
1. Calculate the required amount of water for 3.5 hours:
[tex]\[
y \geq 0.6 \cdot 3.5 + 1.25
\][/tex]
2. Perform the multiplication:
[tex]\[
0.6 \cdot 3.5 = 2.1
\][/tex]
3. Add the reserve amount:
[tex]\[
y \geq 2.1 + 1.25 \quad \rightarrow \quad y \geq 3.35
\][/tex]
4. Compare the given amount of water (3 liters) to the required amount (3.35 liters):
[tex]\[
3 \geq 3.35 \quad \text{(False)}
\][/tex]
Thus, option (c) does not satisfy the inequality.
Conclusion: The situation where Nadine has enough water for her hike is given in option (a): Having 3.2 liters of water for 3 hours of hiking.
