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)

Question

Responses

(10, 5)
(10, 5)

(−3, 5)
(−3, 5)

(2, 5)
(2, 5)

(3, 4.5)

Answer 1

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).