Damon is planning a birthday party for his child. The venue that he has chosen charges \( \$ 65 \) to book the party and \( \$ 19 \) per child. What is the initial value? What is the constant rate? How much does it cost to rent the venue for 5 children?

To analyze the costs associated with the birthday party, we can break it down as follows: 1. **Initial Value**: The initial value is the fixed cost to book the venue, which is \( \$ 65 \). 2. **Constant Rate**: The constant rate is the cost per child, which is \( \$ 19 \). 3. **Cost to Rent the Venue for 5 Children**: To calculate the total cost for 5 children, we can use the formula: \[ \text{Total Cost} = \text{Initial Value} + (\text{Cost per Child} \times \text{Number of Children}) \] Plugging in the values: \[ \text{Total Cost} = 65 + (19 \times 5) \] First, calculate the cost for 5 children: \[ 19 \times 5 = 95 \] Now, add this to the initial value: \[ \text{Total Cost} = 65 + 95 = 160 \] Therefore, the total cost to rent the venue for 5 children is \( \$ 160 \).