Use the following scenario to solve questions 8-10.

Question

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. Which inequality represents the situation described?

(1 point)
Responses

10.50c + 5.50a + 150 ≤ 300
10.50c + 5.50a + 150 ≤ 300

16x + 150 ≤ 300
16x + 150 ≤ 300

10.50c + 5.50a ≤ 300
10.50c + 5.50a ≤ 300

10.50c + 5.50a + 150 ≥ 300

Answer 1

To represent the situation described in the scenario, we first need to understand the components of the costs. The total cost of the birthday party includes a fixed cost of $150, and variable costs that depend on the number of children (c) and adults (a):

• The cost per child is $10.50, which gives us \(10.50c\).
• The cost per adult is $5.50, which gives us \(5.50a\).
• The total cost must not exceed the budget of $300.

The inequality that represents this situation can be constructed as follows:

1. Start with the total cost: total fixed and variable costs. \[ 150 + 10.50c + 5.50a \]
2. Set that total cost less than or equal to the budget of $300: \[ 150 + 10.50c + 5.50a \leq 300 \]
3. To isolate the costs associated with children and adults, rearrange the inequality: \[ 10.50c + 5.50a \leq 300 - 150 \] \[ 10.50c + 5.50a \leq 150 \]

However, since we're looking for the inequality in terms of the total cost including the fixed cost, the correct representation from the options given is:

10.50c + 5.50a + 150 ≤ 300

The correct answer is: 10.50c + 5.50a + 150 ≤ 300.