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. True or false, the party can include 10 children and 5 adults. (1 point) True False

To determine if the party can include 10 children and 5 adults, we need to calculate the total cost.

The fixed cost of the party is $150. The additional costs are as follows:

• Cost per child: $10.50

• Number of children: 10

• Total cost for children: \( 10 \times 10.50 = 105 \)

• Cost per adult: $5.50

• Number of adults: 5

• Total cost for adults: \( 5 \times 5.50 = 27.50 \)

Now, we can calculate the total cost of the party:

\[ \text{Total Cost} = \text{Fixed Cost} + \text{Cost for Children} + \text{Cost for Adults} \]

\[ \text{Total Cost} = 150 + 105 + 27.50 = 282.50 \]

Now, we need to check if the total cost (282.50) does not exceed the budget of $300 and confirms that there is at least one adult and one child.

• Total cost: $282.50 (this is less than $300).
• Number of children: 10 (at least 1).
• Number of adults: 5 (at least 1).

Since all conditions are satisfied, the statement is True.