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)

Question

Responses

(−3,5)
left parenthesis negative 3 comma 5 right parenthesis

(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
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Answer 1

Let's denote the number of adult tickets as "a" and the number of children's tickets as "c".

The total cost of adult tickets is 15a.
The total cost of children's tickets is 12c.

The total cost should not exceed $150, so we can write the inequality:
15a + 12c ≤ 150

To determine which point is a viable solution, we substitute the x and y values of each point into the inequality and check if it is true.

For point (−3,5), we have:
15(-3) + 12(5) = -45 + 60 = 15 ≤ 150
The inequality is true for this point.

For point (3,4.5), we have:
15(3) + 12(4.5) = 45 + 54 = 99 ≤ 150
The inequality is true for this point.

For point (10,5), we have:
15(10) + 12(5) = 150 + 60 = 210 > 150
The inequality is false for this point.

For point (2,5), we have:
15(2) + 12(5) = 30 + 60 = 90 ≤ 150
The inequality is true for this point.

Therefore, the viable solution is (−3,5).