Middle School

A train travels from New York City to Washington, D.C., and then back to New York City. The table shows the number of tickets purchased for each leg of the trip. The cost per ticket is the same for each leg of the trip.

**Destination 1: Washington, D.C.**
- Coach tickets: 150
- Business class tickets: 80
- Money collected (dollars): $22,860

**Destination 2: New York City**
- Coach tickets: 170
- Business class tickets: 100
- Money collected (dollars): $27,280

Write the equations to the system that would explain your answer. Use \(c\) for the cost of a coach ticket and \(b\) for the cost of a business class ticket.

**Destination Washington, D.C. equation:**
\[ 150c + 80b = 22,860 \]

**Destination New York City equation:**
\[ 170c + 100b = 27,280 \]

Answer :

A system of equation is simply a collection of multiple equations

The system of equations is 150c + 80b = 22860, and 170c + 100b = 27280

From the question, we understand that:

  • b represents the cost of business class tickets.
  • c represents the cost of coach tickets.

This means that, the equation of destination 1 would be

150c + 80b = 22860

While the equation of destination 2 would be

170c + 100b = 27280

Hence, the system of equations is 150c + 80b = 22860, and 170c + 100b = 27280

Read more about systems of equations at:

https://brainly.com/question/12895249

Answer: $74

Step-by-step explanation:

Let C represent the cost of a coach ticket

Let B represent the cost of a business ticket

Washington: 150C + 50B = 18,450

NY City: 170C + 100B = 27,280

Solve the system using the Elimination method:

-2(150C + 80B = 18,450) → -300C - 100B = -36,900

1(170C + 100B = 27,280) → 170C + 100B = 27,280

-130C = - 9,620

÷ -130 ÷ -130

C = 74

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