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(2) = 100+15z. 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 32

Ο 28

030

Ο 37

Answer 1

To interpret the linear function model \( b(z) = 100 + 15z \):

• The equation represents the total cost \( b(z) \) for throwing the birthday party, where:
  • \( 100 \) is the fixed cost to rent the bowling alley.
  • \( 15z \) is the variable cost, which depends on the number of people \( z \) attending the party, with each person costing an additional $15.

Leslie received a bill of $550 at the end of the evening. We can set up the equation to find out how many people attended:

\[ b(z) = 550 \]

Substituting the function into the equation gives us:

\[ 100 + 15z = 550 \]

Now, let's solve for \( z \):

1. Subtract 100 from both sides:

\[ 15z = 550 - 100 \] \[ 15z = 450 \]

2. Divide both sides by 15:

\[ z = \frac{450}{15} \] \[ z = 30 \]

This means that a total of 30 people attended the party, including Leslie and Steve.

Since the question asks for the number of other people attending, we need to subtract Leslie and Steve from the total count:

Total attendees: \( 30 \)

Leslie and Steve: \( 2 \)

So the number of other people is:

\[ 30 - 2 = 28 \]

Thus, the answer is:

Ο 28