Question

the senier class at Hartford high school is planning their prom. they've narrowed the location down to two choices. the regal hotel charges, C, $500 for the ballroom rental fee and $75 per student,s, for the meal. the green hill country club charges,C, $1,000 for the ballroom rental fee and $65 per student,s, for the meal. create a pair of linear equations that represents this real world problem.

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let's define the variables:

C = ballroom rental fee
S = cost per student for the meal

For the Regal Hotel:
The ballroom rental fee is $500, so the equation is:

C(regal) = 500

The cost per student for the meal is $75, so the equation is:

S(regal) = 75

For the Green Hill Country Club:
The ballroom rental fee is $1000, so the equation is:

C(green hill) = 1000

The cost per student for the meal is $65, so the equation is:

S(green hill) = 65

Therefore, the pair of linear equations that represents this real-world problem is:

C(regal) = 500
S(regal) = 75

C(green hill) = 1000
S(green hill) = 65

Answer 2

[AI-generated answer — Step-by-Step Bot]

Let's represent the number of students attending the prom as "s" and the total cost as "C".

For the Regal Hotel:
The ballroom rental fee is $500, so it can be represented as 500.
The meal cost per student is $75, so it can be represented as 75s.
Therefore, the total cost at the Regal Hotel can be represented as:
C = 500 + 75s

For the Green Hill Country Club:
The ballroom rental fee is $1,000, so it can be represented as 1000.
The meal cost per student is $65, so it can be represented as 65s.
Therefore, the total cost at the Green Hill Country Club can be represented as:
C = 1000 + 65s

So, the pair of linear equations representing this real-world problem are:

For the Regal Hotel: C = 500 + 75s
For the Green Hill Country Club: C = 1000 + 65s

Answer 3

[AI-generated answer — Explain Bot]

To create a pair of linear equations that represent this real-world problem, we can use the variables C to represent the total cost and S to represent the number of students attending the prom.

For the Regal Hotel:
The ballroom rental fee is $500, which is a fixed cost, so it will not change based on the number of students attending. Therefore, the equation representing the cost at the Regal Hotel can be written as:
C = 500 + 75S

For the Green Hill Country Club:
Similarly, the ballroom rental fee is $1,000, which is again a fixed cost. The meal cost per student is $65, so the equation representing the cost at the Green Hill Country Club can be written as:
C = 1000 + 65S

These equations represent the total cost, C, and the number of students attending, S, for each location option.