Interpret the following linear function model with the given context. Leslie wants to throw a birthday party at their local bowling alley. The space is $100 to rent with an additional charge of $15 per person attending. This scenario of total cost is modeled by the linear function b(x)=100+15x

Question

. Leslie gets a bill of $550 at the end of the evening. In addition to Leslie and Steve, how many other people attended this birthday party?(1 point)
Responses

30
30

37
37

32
32

28

Answer 1

To interpret the given linear function \( b(x) = 100 + 15x \), where \( b(x) \) represents the total cost of the party and \( x \) represents the number of people attending (excluding Leslie and Steve), we can analyze the situation step-by-step.

1. Identify the Costs:

   • The base rental cost of the bowling alley is $100.
   • There is an additional charge of $15 for each person attending the party.

2. Bill at the End of the Evening:

   • At the end of the event, Leslie receives a bill of $550.

3. Set Up the Equation:

   • We know that the total cost \( b(x) \) at the end of the party is $550, so we set up the equation: \[ b(x) = 100 + 15x = 550 \]

4. Solve for \( x \):

   • Start by isolating the variable \( x \): \[ 100 + 15x = 550 \] \[ 15x = 550 - 100 \] \[ 15x = 450 \] \[ x = \frac{450}{15} \] \[ x = 30 \]

5. Interpret the Result:

   • The value \( x = 30 \) represents the number of people attending the party, excluding Leslie and Steve. Since Leslie and Steve are part of the total attendance, we need to add them to find the total number of attendees.

   So, the total number of people who attended the party is: \[ 30 + 2 = 32 \]

Thus, the answer to the question "In addition to Leslie and Steve, how many other people attended this birthday party?" is 30.