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

30
30

37
37

32
32

28
28
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Answer 1

To determine how many people attended the birthday party, we can use the linear function given:

\( b(x) = 100 + 15x \)

where \( b(x) \) is the total cost and \( x \) is the number of people attending (excluding Leslie and Steve).

Given that Leslie received a bill of $550, we set up the equation:

\[
100 + 15x = 550
\]

Now, let's 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 there were 30 additional people attending the party. Since Leslie and Steve are included in the party count but not in the original \( x \), the total number of attendees is:

\[
x + 2 = 30 + 2 = 32
\]

Thus, **the answer is 30 additional people attended the birthday party**.