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)
0 28
0 37
• 30
32

Answer 1

The linear function provided is \( b(x) = 100 + 15x \), where:

- \( b(x) \) represents the total cost of the birthday party,
- \( 100 \) is the fixed rental cost for the bowling alley,
- \( 15 \) is the cost per person attending,
- \( x \) is the number of people attending the party (not including Leslie and Steve).

Leslie received a bill of $550 at the end of the evening. To find out how many people attended the party, we can set up the equation:

\[
b(x) = 550
\]

Substituting in the function:

\[
100 + 15x = 550
\]

Now, we can 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 that 30 people attended the party, excluding Leslie and Steve. Since Leslie and Steve are part of the total number attending, the total number of attendees is:

\[
30 + 2 = 32
\]

Therefore, Leslie and Steve had 30 other people attending the birthday party, so the answer is:

**30** (number of other people who attended).