Question
As people entered the gym for the basketball tournament, members of the pep club were selling raffle tickets. They had $1.50 tickets and $5 tickets. The number of $1.50 tickets sold was two less than four times the number of $5 tickets sold, and the pep club raised $1,152 from the ticket sales. Let x represent the number of $1.50 tickets sold and let y represent the number of $5 tickets sold.
Which equations best represent the situation? Check all that apply.
x = 4y – 2
y = 4x – 2
x + y = 1152
1.5x + 5y = 1152
x = 2 – 4y
y = 2 – 4x
Which equations best represent the situation? Check all that apply.
x = 4y – 2
y = 4x – 2
x + y = 1152
1.5x + 5y = 1152
x = 2 – 4y
y = 2 – 4x
Answers
GPT-4o mini
To represent the situation described, we need to formulate the equations based on the information given.
1. **Relationship between the number of tickets sold:**
The problem states that the number of $1.50 tickets sold (x) is two less than four times the number of $5 tickets sold (y). This can be expressed as:
\[
x = 4y - 2
\]
2. **Total revenue from ticket sales:**
The pep club raised a total of $1,152 from the sales of both types of tickets. The revenue generated from selling $1.50 tickets (x) and $5 tickets (y) can be represented by the equation:
\[
1.5x + 5y = 1152
\]
The other equations provided do not accurately represent the situation:
- **y = 4x - 2**: This is not correct because it reverses the relationship between x and y.
- **x + y = 1152**: This is incorrect because it doesn't take into account the prices of the tickets.
- **x = 2 - 4y**: This is incorrect due to the incorrect relationship between x and y.
- **y = 2 - 4x**: This is also incorrect due to the incorrect relationship.
Thus, the correct equations that best represent the situation are:
- \( x = 4y - 2 \)
- \( 1.5x + 5y = 1152 \)
1. **Relationship between the number of tickets sold:**
The problem states that the number of $1.50 tickets sold (x) is two less than four times the number of $5 tickets sold (y). This can be expressed as:
\[
x = 4y - 2
\]
2. **Total revenue from ticket sales:**
The pep club raised a total of $1,152 from the sales of both types of tickets. The revenue generated from selling $1.50 tickets (x) and $5 tickets (y) can be represented by the equation:
\[
1.5x + 5y = 1152
\]
The other equations provided do not accurately represent the situation:
- **y = 4x - 2**: This is not correct because it reverses the relationship between x and y.
- **x + y = 1152**: This is incorrect because it doesn't take into account the prices of the tickets.
- **x = 2 - 4y**: This is incorrect due to the incorrect relationship between x and y.
- **y = 2 - 4x**: This is also incorrect due to the incorrect relationship.
Thus, the correct equations that best represent the situation are:
- \( x = 4y - 2 \)
- \( 1.5x + 5y = 1152 \)