Final answer:
The appropriate inequality for Julia's budget situation is 5 + 2.75 · S ≤ 21. Solve it by subtracting 5 from both sides and then dividing by 2.75, yielding that Julia can afford up to 5 train stops.
Step-by-step explanation:
The student is asking which inequality represents the scenario where Julia has $21 for a train ticket, with an initial fee of $5 and an additional fee of $2.75 per stop (S). To solve the mathematical problem completely, we need to set up an equation that accounts for Julia's budget and the ticket pricing structure. The correct inequality that describes the scenario is 5 + 2.75 · S ≤ 21. This inequality dictates that when you add 5 dollars to 2.75 times the number of stops (S), it should be less than or equal to 21 dollars, which is the total amount of money Julia has for the train ticket.
To determine the largest number of stops Julia can afford, we need to manipulate the inequality:
Subtract 5 from both sides of the inequality to isolate the variable term on one side: 2.75 · S ≤ 16.
Divide both sides by 2.75 to solve for S: S ≤ 16 / 2.75.
Calculate the quotient to find the maximum number of stops: S ≤ 5.818.
Since Julia cannot buy a fraction of a stop, she can afford a maximum of 5 stops.