Question

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
. 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

32
32

28
28

30
30

37

Answer 1

To determine how many additional people attended the birthday party, we will start by analyzing the linear function provided: \( b(x) = 100 + 15x \).

In this function:
- \( b(x) \) is the total cost for the party.
- \( 100 \) is the fixed cost for renting the space.
- \( 15x \) represents the variable cost, where \( x \) is the number of people attending (excluding Leslie and Steve).

Leslie received a bill for $550 at the end of the evening. Therefore, we can set up the equation:

\[ 100 + 15x = 550 \]

Next, we'll solve for \( x \):

1. Subtract 100 from both sides:

\[ 15x = 550 - 100 \]
\[ 15x = 450 \]

2. Divide both sides by 15:

\[ x = \frac{450}{15} \]
\[ x = 30 \]

This means 30 additional people attended the party. Since Leslie and Steve are not included in this count, the total number of attendees is \( 30 + 2 = 32 \).

Thus, the answer to the number of additional people who attended the birthday party, excluding Leslie and Steve, is **30**.