Question

Use the following scenario to solve questions 8-10. 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) 10.50c+5.50a+150≤ 300 16x+150≤ 300 10.50c+5.50a≤ 300 10.50c+5.50a+150≥ 300

Answer 1

To represent the situation described in the scenario, we need to account for the total cost of the party including the fixed cost and the variable costs associated with the number of children and adults attending.

1. **Fixed Cost:** $150
2. **Cost Per Child:** $10.50 (let's denote the number of children as \( c \))
3. **Cost Per Adult:** $5.50 (let's denote the number of adults as \( a \))
4. **Total Budget:** $300

The total cost of the party needs to be less than or equal to the budget of $300. Therefore, we can express this relationship as follows:

\[
150 + 10.50c + 5.50a \leq 300
\]

To isolate the variable costs on one side, we can subtract 150 from both sides:

\[
10.50c + 5.50a \leq 300 - 150
\]

This simplifies to:

\[
10.50c + 5.50a \leq 150
\]

Thus, the correct inequality that represents the situation described is:

**10.50c + 5.50a + 150 ≤ 300**

This captures the costs associated with the number of children and adults at the party while ensuring that the total cost does not exceed the budget. So, the correct answer is:

**10.50c + 5.50a + 150 ≤ 300**.