The senior 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 Greenhill 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 represent this real-world problem.

Question

The senior 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 Greenhill 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 represent this real-world problem.

Answer 1

Let R represent the total cost at the Regal Hotel and G represent the total cost at the Greenhill Country Club.

For the Regal Hotel:
R = 500 + 75s

For the Greenhill Country Club:
G = 1000 + 65s

Answer 2

The Jackson Jammers are giving away bags and caps at their next game. The bags, b , cost them $10 each, and the caps, c , cost them $5 each. They plan to give away 2,000 total items and have a budget of $12,500. Write the pair of linear equations that model this situation.(1 point) Responses b+c=12,500 ; 5b+10c=2,000 b plus c equals 12,500 ; 5 b plus 10 c equals 2,000 b+c=2,000 ; 5b+10c=12,500 b plus c equals 2,000 ; 10 b plus 10 c equals 12,500 b+c=2,000 ; 10b+5c=12,500 b plus c equals 2,000 ; 10 b plus 5 c equals 12,500 b+c=12,500 ; 10b+5c=2,000

Answer 3

Let's define the variables:

- C: total cost
- s: number of students attending the prom

Now, let's create the equations:

Equation 1 (Regal Hotel):
C = 500 + 75s

Equation 2 (Greenhill Country Club):
C = 1000 + 65s

These equations represent the total cost, C, in terms of the number of students attending, s, for each venue option.

Answer 4

To create a pair of linear equations that represent this real-world problem, we can use the following variables:

Let's denote:
C as the total cost (in dollars) of renting the ballroom
S as the number of students attending the prom

For the Regal Hotel, the equation would be:

C = 500 + 75S

Here, we have the fixed rental fee of $500 and an additional charge of $75 per student for the meal.

For the Greenhill Country Club, the equation would be:

C = 1000 + 65S

Similarly, here we have a rental fee of $1000 and an additional charge of $65 per student for the meal.

Now, we have a pair of linear equations that represent this real-world problem:

For the Regal Hotel: C = 500 + 75S
For the Greenhill Country Club: C = 1000 + 65S