Question

The price of a train ticket consists of an initial fee of $5 plus a fee of $2.75 per stop. Julia has $21 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 S represent the number of stops that Julia buys.
Which inequality describes this scenario?
a.5+2.75⋅S≤21
b.5+2.75⋅S≥21
c.5+2.75⋅S≤50
d.5+2.75⋅S≥50

Answer 1

The inequality that describes how many stops Julia can afford given her budget and the price structure of the train ticket is 5 + 2.75 × S ≤ 21, representing the initial fee plus the cost per stop being less than or equal to her $21 budget.

Step-by-step explanation:

The scenario presented is a mathematical problem involving linear inequalities. Julia wishes to know the largest number of stops she can afford for a train journey given her budget of $21. The cost of the ticket is composed of an initial fixed fee of $5 with an additional fee of $2.75 for each stop. To represent this mathematically, let S be the number of stops, then the total cost is the sum of the initial fee plus the product of $2.75 and S. Thus, the inequality that describes Julia's situation would be the total cost being less than or equal to her budget, which is represented as 5 + 2.75 × S ≤ 21. This inequality checks for the maximum value of S that will not exceed Julia's budget.