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?
(3, 4.5)
(2, 5)
(10, 5)
(-3, 5)

Answer 1

Let A = number of adult tickets and C = number of children’s tickets. The cost constraint is
15A + 12C ≤ 150.

Contextual constraints: A and C must be whole nonnegative numbers (A, C ∈ Z≥0). From the cost alone you also get A ≤ 10 and C ≤ 12 (since 15A ≤ 150 and 12C ≤ 150).

Check the points:
- (3, 4.5): satisfies the cost (45 + 54 = 99 ≤ 150) but C = 4.5 is not allowed (can't buy half a ticket) → not viable.
- (2, 5): 30 + 60 = 90 ≤ 150 and both are nonnegative integers → viable.
- (10, 5): 150 + 60 = 210 > 150 → not viable.
- (-3, 5): negative adults not allowed (and A must be ≥ 0) → not viable.

Only (2, 5) is a viable solution.