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?

Answer 1

To interpret the linear function \( b(x) = 100 + 15x \), we can break down its components in the context of Leslie's birthday party:

- The term \( 100 \) represents the fixed cost to rent the bowling alley. This is the base cost, regardless of how many people attend the party.
- The term \( 15x \) represents the variable cost that depends on the number of attendees, where \( x \) is the number of people attending the party (excluding Leslie and Steve). The \( 15 \) indicates that there is an additional charge of \( $15 \) for each person attending.

Now, Leslie received a bill of \( $550 \) at the end of the evening. We can set up the equation based on the total cost:

\[
b(x) = 550
\]

Substituting the linear function into this equation gives:

\[
100 + 15x = 550
\]

Next, we can 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, \( x = 30 \) means that there were 30 people attending the party in addition to Leslie and Steve.

To find the total number of attendees, we need to add Leslie and Steve:

\[
\text{Total attendees} = x + 2 = 30 + 2 = 32
\]

In summary, in addition to Leslie and Steve, **30 other people attended the birthday party**.