The price of a train ticket consists of an initial fee of [tex]\[tex]$5[/tex] plus a fee of [tex]\$[/tex]2.75[/tex] per stop. Julia has [tex]\$21[/tex] and would like to travel 50 kilometers. She wants to know the largest number of stops she can afford to buy on a ticket.

Let [tex]S[/tex] represent the number of stops that Julia buys.

1. Which inequality describes this scenario?

A. [tex]5 + 2.75 \cdot S \leq 21[/tex]



Answer :

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.