Question
Using your answer/work from the above question: "The Ramirez family is going to the space museum. Adult tickets are $15 and children's tickets are $12. They want to spend a maximum of $150. Write a two-variable inequality to model this situation and determine the contextual constraints." Which of the following points is a viable solution? (1 point)
Responses
(10, 5)
(10, 5)
(−3, 5)
(−3, 5)
(2, 5)
(2, 5)
(3, 4.5)
Responses
(10, 5)
(10, 5)
(−3, 5)
(−3, 5)
(2, 5)
(2, 5)
(3, 4.5)
Answers
GPT-4o mini
To model the situation with a two-variable inequality, we can let:
- \( x \) represent the number of adult tickets purchased.
- \( y \) represent the number of children's tickets purchased.
The cost of adult tickets is $15 each, and the cost of children's tickets is $12 each, and the family wants to spend a maximum of $150. Thus, we can write the inequality as follows:
\[ 15x + 12y \leq 150 \]
Next, we also need to consider the contextual constraints. Since the number of tickets cannot be negative, we have the following constraints:
1. \( x \geq 0 \) (number of adult tickets cannot be negative)
2. \( y \geq 0 \) (number of children's tickets cannot be negative)
Now, we can evaluate the given points to see which ones satisfy the inequality \( 15x + 12y \leq 150 \) and the constraints:
1. **Point (10, 5)**:
- \( 15(10) + 12(5) = 150 + 60 = 210 \) (not viable)
2. **Point (−3, 5)**:
- Invalid since \( x \) cannot be negative (not viable)
3. **Point (2, 5)**:
- \( 15(2) + 12(5) = 30 + 60 = 90 \) (90 ≤ 150; viable)
4. **Point (3, 4.5)**:
- \( 15(3) + 12(4.5) = 45 + 54 = 99 \) (99 ≤ 150; viable)
The viable solutions from the list are **(2, 5)** and **(3, 4.5)**. However, since the constraints state that \( x \) and \( y \) must be whole numbers (you can't have a fraction of a ticket), the only viable option that fits whole numbers is **(2, 5)**.
Thus, the answer is **(2, 5)**.
- \( x \) represent the number of adult tickets purchased.
- \( y \) represent the number of children's tickets purchased.
The cost of adult tickets is $15 each, and the cost of children's tickets is $12 each, and the family wants to spend a maximum of $150. Thus, we can write the inequality as follows:
\[ 15x + 12y \leq 150 \]
Next, we also need to consider the contextual constraints. Since the number of tickets cannot be negative, we have the following constraints:
1. \( x \geq 0 \) (number of adult tickets cannot be negative)
2. \( y \geq 0 \) (number of children's tickets cannot be negative)
Now, we can evaluate the given points to see which ones satisfy the inequality \( 15x + 12y \leq 150 \) and the constraints:
1. **Point (10, 5)**:
- \( 15(10) + 12(5) = 150 + 60 = 210 \) (not viable)
2. **Point (−3, 5)**:
- Invalid since \( x \) cannot be negative (not viable)
3. **Point (2, 5)**:
- \( 15(2) + 12(5) = 30 + 60 = 90 \) (90 ≤ 150; viable)
4. **Point (3, 4.5)**:
- \( 15(3) + 12(4.5) = 45 + 54 = 99 \) (99 ≤ 150; viable)
The viable solutions from the list are **(2, 5)** and **(3, 4.5)**. However, since the constraints state that \( x \) and \( y \) must be whole numbers (you can't have a fraction of a ticket), the only viable option that fits whole numbers is **(2, 5)**.
Thus, the answer is **(2, 5)**.