The party will cost $150, plus $10.50 per child and $5.50 per adult. There needs to be at least one adult and one child at the party, and the cost cannot exceed $300. (14.286, 0) is a viable solution for the above situation. Consider the ordered pair as (c,a) where c represents number of children and a represents number of adults at the party. (1 point) True False

1 answer

To evaluate whether the ordered pair (14.286, 0) is a viable solution for the given cost situation, we need to analyze the constraints provided:

  1. The total cost equation is given by: Total Cost=150+10.50c+5.50a where c is the number of children and a is the number of adults.

  2. The conditions specify:

    • There must be at least one adult (a1).
    • There must be at least one child (c1).
    • The total cost cannot exceed $300.

Substituting the ordered pair (14.286, 0):

  • c=14.286 (approximately 14 children)
  • a=0 (0 adults)

Now verifying the conditions:

  • Total cost: Total Cost=150+10.50(14.286)+5.50(0)=150+150.003=300.003 This exceeds $300, which is not allowed.

  • Number of adults: The number of adults a=0, which violates the condition of having at least one adult.

  • Number of children: The number of children can be roughly 14.286, which satisfies the condition of having at least one child.

Since a must be at least 1 and the cost exceeds $300, (14.286, 0) is not a viable solution.

Thus, the answer is False.