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.

True or false, the party can include 10 children and 5 adults.

(1 point)
Responses

True
True

False

Answer 1

To determine whether the party can include 10 children and 5 adults within the budget, let's calculate the total cost.

1. Fixed cost: $150
2. Cost per child: $10.50
3. Cost per adult: $5.50

Now, calculate the total cost for 10 children and 5 adults:

• Cost for 10 children: \( 10 \times 10.50 = 105 \)
• Cost for 5 adults: \( 5 \times 5.50 = 27.50 \)

Now, add these costs together with the fixed cost:

Total cost = Fixed cost + Cost for children + Cost for adults Total cost = \( 150 + 105 + 27.50 = 282.50 \)

Now, check if this total exceeds the budget of $300:

Total cost = $282.50, and the budget is $300. Since $282.50 is less than $300 and also fulfills the requirement of having at least one adult and one child, the answer is:

True.