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 oine child at the party, andn 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 andn a represents number of adults ath the party.
true
false

Answer 1

To determine if the ordered pair (14.286, 0) is a viable solution for the party cost constraints, we need to apply the conditions given:

1. **Cost formula**: The total cost \( C \) for the party is given by:
\[
C = 150 + 10.50c + 5.50a
\]
where \( c \) is the number of children and \( a \) is the number of adults.

2. **Constraints**:
- At least one adult: \( a \geq 1 \)
- At least one child: \( c \geq 1 \)
- Total cost cannot exceed $300: \( C \leq 300 \)

Now, substituting \( c = 14.286 \) and \( a = 0 \):

1. **Check the number of adults**: \( a = 0 \) does not satisfy the constraint of having at least one adult.

2. **Cost calculation**:
\[
C = 150 + 10.50(14.286) + 5.50(0)
\]
\[
C = 150 + 10.50 \times 14.286
\]
\[
C \approx 150 + 150 = 300
\]
The cost calculation shows that it meets the cost constraint of not exceeding $300, but since there are no adults, this ordered pair does not satisfy the constraints.

Given that one of the primary constraints (having at least one adult) is not met, the statement is **false**.

Therefore, the answer is **false**.