Question

Meha is helping her aunt to plan a birthday party for her cousin at the science center. He 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 at least one child at the party. She has budgeted $300 for the party and that is the maximum amount she wants to spend. Let c = the number of children and a = the number of adults. Which inequality represents this situation? (1 point) Responses 10.5a + 5.5c ≤ 300 10.5a + 5.5c ≤ 300 5.5c + 10.5a ≤ 300 5.5c + 10.5a ≤ 300 150 + 10.5c + 5.5a ≤ 300 150 + 10.5c + 5.5a ≤ 300 150 + 10.5a + 5.5c ≤ 300

Answer 1

To represent the situation mathematically, we need to account for the cost components as described. The total cost of the party includes:

• A fixed cost of $150
• A variable cost of $10.50 per child (c)
• A variable cost of $5.50 per adult (a)

The total cost can be expressed as:

\[ \text{Total Cost} = 150 + 10.50c + 5.50a \]

Meha's aunt has a budget of $300 for the party, which gives us the inequality:

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

This inequality captures the situation that the total cost must not exceed the budget of $300.

Additionally, We also know that there must be at least one adult and one child present, which means:

\[ c \geq 1 \quad \text{and} \quad a \geq 1 \]

However, the primary inequality reflecting the budget constraint is:

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

Thus, the correct response from the options provided is:

150 + 10.5c + 5.5a ≤ 300