Let's break down the problem to find a suitable inequality that describes the given scenario.
1. The total cost of the train ticket is made up of two components:
- An initial fee of [tex]$5.
- An additional fee of $[/tex]2.75 per stop.
2. Julia has a total of [tex]$21 to spend on the ticket.
We are asked to determine the largest number of stops, denoted by \( S \), that Julia can afford, given her budget constraint.
The cost of the ticket in terms of the number of stops (\( S \)) can be modeled as:
\[ \text{Total Cost} = 5 + 2.75 \cdot S \]
Julia's budget constraint is that the total cost should not exceed $[/tex]21. Therefore, the inequality that represents this situation is:
[tex]\[ 5 + 2.75 \cdot S \leq 21 \][/tex]
So, the correct inequality is:
(A) [tex]\( 5 + 2.75 \cdot S \leq 21 \)[/tex]
To verify the largest number of stops Julia can afford, we need to solve this inequality for [tex]\( S \)[/tex].
Rewriting the inequality:
[tex]\[ 5 + 2.75 \cdot S \leq 21 \][/tex]
Subtract 5 from both sides:
[tex]\[ 2.75 \cdot S \leq 16 \][/tex]
Next, divide both sides by 2.75:
[tex]\[ S \leq \frac{16}{2.75} \][/tex]
This results in:
[tex]\[ S \leq 5.818181818181818 \][/tex]
Thus, the largest number of whole stops Julia can afford is 5, as she cannot purchase a fraction of a stop.
In summary, option (A) [tex]\( 5 + 2.75 \cdot S \leq 21 \)[/tex] correctly describes the scenario, and the largest number of stops Julia can afford, based on her budget, is 5 stops.
