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

30
30

32
32

37
37

28
28
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Answer 1

To determine how many people attended the birthday party, we can use the linear function model given for the total cost \( b(x) = 100 + 15x \), where \( x \) is the number of people attending (excluding Leslie and Steve).

Leslie received a bill of $550. We need to set the function equal to this amount and solve for \( x \):

\[ b(x) = 550 \] \[ 100 + 15x = 550 \]

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, \( x = 30 \) represents the number of people attending in addition to Leslie and Steve.

Since Leslie and Steve are also attending, we need to add them to this number:

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

Thus, the total number of other people who attended the birthday party, excluding Leslie and Steve, is 30.