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

Question

. 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 find out how many people attended Leslie's birthday party, we can use the linear function provided, which models the total cost \( b(x) \):

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

In this function, \( b(x) \) is the total cost, \( 100 \) is the flat rental cost of the bowling alley, and \( 15x \) represents the additional cost for \( x \) people attending (where \( x \) is the number of additional attendees, not counting Leslie and Steve).

Leslie received a bill of \( 550 \), so we can set up the following equation:

\[ 100 + 15x = 550 \]

Now, we can solve for \( x \):

1. Subtract \( 100 \) from both sides:

\[ 15x = 550 - 100 \]

\[ 15x = 450 \]

2. Divide both sides by \( 15 \):

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

\[ x = 30 \]

So, the value of \( x \) (the number of additional people attending) is \( 30 \).

Since Leslie and Steve attended the party as well, we need to add them to the total number of attendees:

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

Thus, the answer is that 32 people attended the birthday party (including Leslie and Steve).

The correct response is:

32