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

37
37

32
32

28
28

30

Answer 1

To solve the problem, we start with the linear function for the total cost of the birthday party:

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

where:
- \( b(x) \) is the total cost,
- \( 100 \) is the fixed rental fee for the bowling alley,
- \( 15 \) is the cost per person,
- \( x \) is the number of people attending the party.

Leslie received a bill for $550. We can set up the equation:

\[
550 = 100 + 15x
\]

Next, we solve for \( x \):

1. Subtract 100 from both sides:

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

2. Divide both sides by 15:

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

This means that there were 30 people total attending the birthday party.

Since the question specifies that in addition to Leslie and Steve, we need to find out how many other people attended. We subtract Leslie and Steve from the total:

\[
30 - 2 = 28
\]

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