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

30
30

32
32

37

Answer 1

To determine how many additional people attended the birthday party, we can use the given linear cost function \( b(x) = 100 + 15x \), where:

• \( b(x) \) is the total cost of the party,
• \( 100 \) is the rental fee for the space,
• \( 15 \) is the cost per person attending,
• \( x \) is the number of additional attendees (excluding Leslie and Steve).

We know that Leslie received a bill of $550:

\[ b(x) = 550 \]

Now, we can set up the equation:

\[ 100 + 15x = 550 \]

Next, we'll solve for \( x \):

1. Subtract 100 from both sides: \[ 15x = 550 - 100 \] \[ 15x = 450 \]

2. Divide both sides by 15: \[ x = \frac{450}{15} \] \[ x = 30 \]

Since Leslie and Steve are already counted, the total number of people that attended the party is \( x + 2 \) (the two of them), which is:

\[ 30 + 2 = 32 \]

Thus, the number of other attendees (excluding Leslie and Steve) is 30.

Therefore, the answer is 30.