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

28
28

37
37

30
30

32

Answer 1

To determine how many people attended Leslie's birthday party using the given linear function model \( b(x) = 100 + 15x \), where \( x \) represents the number of people attending the party, we start by setting the total cost equal to the bill received.

Leslie received a bill of $550, so we can set up the equation:

\[
b(x) = 550
\]

Substituting the function into the equation gives:

\[
100 + 15x = 550
\]

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

1. Subtract 100 from both sides:

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

2. Now, divide both sides by 15:

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

Thus, there were 30 people in total at the party. However, since the question specifies "In addition to Leslie and Steve," we need to subtract the 2 known attendees from the total:

\[
\text{Number of other people} = x - 2 = 30 - 2 = 28
\]

Therefore, the number of other people who attended the birthday party is **28**.