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)

Question

Ο 37

Ο 32

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Ο 28

30

Answer 1

To interpret the linear function model representing the total cost \( b(x) = 100 + 15x \), we can break down the components:

• The fixed cost of renting the bowling alley is $100.
• The variable cost is $15 for each person attending the party, represented by \( x \).

Leslie received a bill of $550. To find out how many people attended the party, we can set up the equation based on the total cost:

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

Setting \( b(x) \) equal to 550, we have:

\[ 550 = 100 + 15x \]

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

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

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

Thus, the total number of people that attended the birthday party is \( x = 30 \).

Given that Leslie and Steve are included in this count, we need to subtract the 2 of them to find how many additional people attended:

\[ 30 - 2 = 28 \]

Therefore, the number of additional people attending the party (beyond Leslie and Steve) is 28.

Answer: 28