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

Answer 1

Let's define the variables:

• Let \( x \) represent the number of adult tickets.
• Let \( y \) represent the number of children's tickets.

The cost of the tickets can be expressed as:

• The cost of adult tickets is \( 15x \).
• The cost of children's tickets is \( 12y \).

The Ramirez family wants to spend a maximum of $150. This gives us the inequality:

\[ 15x + 12y \leq 150 \]

Now, let's assume that \( x \) (the number of adults) and \( y \) (the number of children) need to be non-negative. Therefore, we also have the constraints:

\[ x \geq 0 \ y \geq 0 \]

So, the complete set of inequalities is:

1. \( 15x + 12y \leq 150 \)
2. \( x \geq 0 \)
3. \( y \geq 0 \)

Now, let's determine which of the points is a viable solution:

1. For the point (3, 4.5): \[ 15(3) + 12(4.5) = 45 + 54 = 99 \leq 150 \quad \text{(Valid)} \]

2. For the point (10, 5): \[ 15(10) + 12(5) = 150 + 60 = 210 \nleq 150 \quad \text{(Not valid)} \]

3. For the point (2, 5): \[ 15(2) + 12(5) = 30 + 60 = 90 \leq 150 \quad \text{(Valid)} \]

4. For the point (-3, 5): Negative values for tickets are not possible, so we disregard this point.

Conclusion:

The points (3, 4.5) and (2, 5) are valid solutions, but because we usually deal with whole numbers in context like this (assuming they represent actual tickets), the output (3, 4.5) would not be typical since we can't buy half a ticket.

The best valid point representing a possible viable solution is:

• (2, 5).

Thus, the viable solutions to the problem are the integer points such as (2, 5), while (3, 4.5) implies purchasing a non-integer number of tickets.