Tickets to the 3-D showing of a certain movie cost $2.00
more than tickets to the regular showing. Oliver bought five regular tickets and four 3-D tickets, and the total cost was $89
.

Which system of equations can be used to determine the price of a regular ticket, x
, and the price of a 3-D ticket, y
?
A.
x=y+2
5x+4y=89

B.
y=x+2
4x+5y=89

C.
x+y=2
4x+5y=89

D.
y=x+2
5x+4y=89

To determine which system of equations can be used to solve this problem, let's break it down:

1. Let **x** be the price of a regular ticket.
2. Let **y** be the price of a 3-D ticket.

The problem tells us:
- The 3-D ticket costs $2.00 more than the regular ticket. This gives us the relationship between the two prices:  
  **y = x + 2**
  
- Oliver bought five regular tickets and four 3-D tickets, and the total cost was $89. This gives us another equation:  
  **5x + 4y = 89**

Now, looking at the options:

**A.**
- **x = y + 2**
- **5x + 4y = 89**  
This is incorrect because it incorrectly says the regular ticket costs $2.00 more than the 3-D ticket.

**B.**
- **y = x + 2**
- **4x + 5y = 89**  
This is incorrect because the second equation should be **5x + 4y = 89** (Oliver bought 5 regular tickets and 4 3-D tickets, not 4 regular and 5 3-D).

**C.**
- **x + y = 2**
- **4x + 5y = 89**  
This is incorrect because the first equation incorrectly says the sum of the two ticket prices is $2.00, which isn't true.

**D.**
- **y = x + 2**
- **5x + 4y = 89**  
This is correct. It correctly states that the 3-D ticket is $2 more than the regular ticket and uses the right combination of tickets.

Thus, the correct answer is **D**.

Would you like more details on solving this system or any other questions?

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Here are 5 related questions:
1. How do you solve a system of equations using substitution?
2. How can you graphically represent the solution of a system of equations?
3. What happens if two equations in a system are parallel?
4. How do you solve a system of equations using the elimination method?
5. What is the difference between dependent, independent, and inconsistent systems of equations?

**Tip**: When solving a system of equations, always verify that both equations are consistent with the problem's conditions.

Tickets to the 3-D showing of a certain movie cost $2.00 more than tickets to the regular showing. Oliver bought five regular tickets and four 3-D tickets, and the total cost was $89. Which system of equations can be used to determine the price of a regular ticket, x, and the price of a 3-D ticket, y?

Solve a system of linear equations to determine the price of regular and 3-D movie tickets. Learn how to apply the substitution method to solve the equations y = x + 2 and 5x + 4y = 89. Suitable for students in Grades 8-10, this problem covers algebraic concepts and systems of equations.

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