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 inequility to model this situation and determine the contextual constraints. Which of the following points is variable solution?

Question

A. (10, 5)
B. (-3, 5)
C. (3, 4.5)
D. (2, 5)

Answer 1

Let's assume x represents the number of adult tickets and y represents the number of children's tickets.

The cost of adult tickets is $15x, and the cost of children's tickets is $12y.

The total amount spent must be less than or equal to $150, so we can write the inequality:

15x + 12y ≤ 150

Now, let's analyze the given points:

A. (10, 5)
If we substitute x = 10 and y = 5 into the inequality, we get:
15(10) + 12(5) = 150 + 60 = 210
210 is greater than 150, so this point is not a valid solution.

B. (-3, 5)
We cannot have a negative number of adult tickets, so this point is not a valid solution.

C. (3, 4.5)
If we substitute x = 3 and y = 4.5 into the inequality, we get:
15(3) + 12(4.5) = 45 + 54 = 99
99 is less than 150, so this point is a valid solution.

D. (2, 5)
If we substitute x = 2 and y = 5 into the inequality, we get:
15(2) + 12(5) = 30 + 60 = 90
90 is less than 150, so this point is also a valid solution.

The variable solutions for the inequality are C. (3, 4.5) and D. (2, 5).