Meha is helping her aunt to plan a birthday party for her cousin at the science center. Her aunt tells her that 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. She has budgeted $300 for the party and that is the maximum amount she wants to spend.

Question

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)
Responses

True
True

False

Answer 1

To determine if the ordered pair (14.286, 0) is a viable solution for the party cost scenario, we need to analyze the requirements and the cost equation.

The given conditions are:

• The total cost of the party is calculated as follows: \[ \text{Total Cost} = 150 + 10.50c + 5.50a \]
• The maximum budget for the party is $300.
• There needs to be at least one adult (a ≥ 1) and one child (c ≥ 1) at the party.

Now, let's evaluate the ordered pair (14.286, 0):

• Here, c = 14.286 (number of children) and a = 0 (number of adults).

Since the conditions specify that there must be at least one adult and one child, the value a = 0 does not satisfy the requirement. Therefore, (14.286, 0) is not a viable solution.

Thus, the answer is False.