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
28
28
30
30
32
32
37
. 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
Answers
GPT-4o mini
To determine how many additional people attended Leslie's birthday party, we start with the linear cost function provided:
\[
b(x) = 100 + 15x
\]
where:
- \( b(x) \) is the total cost,
- \( 100 \) is the fixed rental cost,
- \( 15 \) is the cost per person,
- \( x \) is the number of people attending (excluding Leslie and Steve).
Leslie received a bill of $550 at the end of the evening. We can set up the equation:
\[
550 = 100 + 15x
\]
Next, we will solve this equation for \( x \):
1. Subtract 100 from both sides:
\[
550 - 100 = 15x \\
450 = 15x
\]
2. Divide both sides by 15:
\[
x = \frac{450}{15} = 30
\]
This means there were 30 people attending in total excluding Leslie and Steve. Since Leslie and Steve are part of the total count, we need to add them to find the total number of attendees:
\[
\text{Total attendees} = 30 + 2 = 32
\]
Therefore, in addition to Leslie and Steve, the number of other people that attended the party is:
\[
\text{Other attendees} = x = 30
\]
The correct answer is 30.
\[
b(x) = 100 + 15x
\]
where:
- \( b(x) \) is the total cost,
- \( 100 \) is the fixed rental cost,
- \( 15 \) is the cost per person,
- \( x \) is the number of people attending (excluding Leslie and Steve).
Leslie received a bill of $550 at the end of the evening. We can set up the equation:
\[
550 = 100 + 15x
\]
Next, we will solve this equation for \( x \):
1. Subtract 100 from both sides:
\[
550 - 100 = 15x \\
450 = 15x
\]
2. Divide both sides by 15:
\[
x = \frac{450}{15} = 30
\]
This means there were 30 people attending in total excluding Leslie and Steve. Since Leslie and Steve are part of the total count, we need to add them to find the total number of attendees:
\[
\text{Total attendees} = 30 + 2 = 32
\]
Therefore, in addition to Leslie and Steve, the number of other people that attended the party is:
\[
\text{Other attendees} = x = 30
\]
The correct answer is 30.