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?

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 ≥ 0 and c ≥ 0 (you cannot buy a negative number of tickets).
- a and c must be whole numbers (integers) since tickets are indivisible.
- From the budget you also get the individual upper bounds a ≤ 10 and c ≤ 12 (because 15·10 = 150 and 12·13 = 156 > 150).

To test any candidate point (a,c): substitute into 15a + 12c and verify the sum is ≤ 150 and that a,c are nonnegative integers. Examples:
- (10,0): 15·10 + 12·0 = 150 → viable.
- (6,5): 15·6 + 12·5 = 90 + 60 = 150 → viable.
- (0,12): 0 + 144 = 144 → viable.
- (5,8): 75 + 96 = 171 → not viable.

If you have the list of points from the problem, give them and I’ll check each one.