111k views
0 votes
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. Which inequality describes this scenario?

A) 5+2.75xS <=21
B) 5+2.75xS >=21
C) 5+2.75xS <=50
D) 5+2.75xS >=50

1 Answer

4 votes

Answer:

The inequality that describes this scenario is A) 5+2.75xS <=21.

To explain why, let’s define some variables:

  • S is the number of stops that Julia can afford to buy on a ticket.

  • D is the distance that Julia can travel with a ticket.

  • P is the price of a ticket.

The problem gives us the following information:

  • The price of a ticket consists of an initial fee of $5 plus a fee of $2.75 per stop. This means that P = 5 + 2.75S.

  • Julia has $21 and would like to travel 50 kilometers. This means that P <= 21 and D = 50.

We want to find the largest number of stops that Julia can afford to buy on a ticket. This means that we want to maximize S subject to the constraints of P <= 21 and D = 50.

To do this, we can use the following steps:

  • Substitute P = 5 + 2.75S into P <= 21 and solve for S. This gives us 5 + 2.75S <= 21, which simplifies to S <= 5.82. This means that Julia can afford at most 5 stops on a ticket.

  • Substitute S = 5 into P = 5 + 2.75S and find the corresponding price. This gives us P = 5 + 2.75(5), which simplifies to P = 18.75. This means that Julia can buy a ticket for $18.75 with 5 stops.

  • Substitute S = 5 into D = 50 and find the corresponding distance. This gives us D = 50, which means that Julia can travel exactly 50 kilometers with 5 stops.

Therefore, the largest number of stops that Julia can afford to buy on a ticket is 5, and the corresponding price and distance are $18.75 and 50 kilometers, respectively.

The inequality that describes this scenario is A) 5+2.75xS <=21, because it shows the relationship between the price of a ticket and the number of stops that Julia can afford. The other inequalities are either incorrect or irrelevant to the problem.

User Akash Ranjan
by
7.0k points