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 (3,4.5) left parenthesis 3 comma 4.5 right parenthesis (−3,5) left parenthesis negative 3 comma 5 right parenthesis (10,5) left parenthesis 10 comma 5 right parenthesis (2,5)

Answer 1

Let's say the number of adult tickets is represented by the variable A, and the number of children's tickets is represented by the variable C.

The cost of adult tickets is $15, so the total cost of adult tickets is 15A.
The cost of children's tickets is $12, so the total cost of children's tickets is 12C.
The total amount spent is the sum of the cost of adult tickets and the cost of children's tickets, which is 15A + 12C.
The problem states that they want to spend a maximum of $150, so we can create the inequality:
15A + 12C ≤ 150.

Now let's test each point to see if it satisfies the inequality:

1. (3, 4.5)
Plugging in A = 3 and C = 4.5:
15(3) + 12(4.5) = 45 + 54 = 99.
99 is less than 150, so this point satisfies the inequality.

2. (-3, 5)
Plugging in A = -3 and C = 5:
15(-3) + 12(5) = -45 + 60 = 15.
15 is less than 150, so this point satisfies the inequality.

3. (10, 5)
Plugging in A = 10 and C = 5:
15(10) + 12(5) = 150 + 60 = 210.
210 is greater than 150, so this point does not satisfy the inequality.

4. (2, 5)
Plugging in A = 2 and C = 5:
15(2) + 12(5) = 30 + 60 = 90.
90 is less than 150, so this point satisfies the inequality.

Therefore, the viable solution is (3, 4.5).