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.(1 point) Responses Regal Hotel: C=500s+75; Greenhill Country Club: C=1,000s+65 Regal Hotel: upper C equals 500 s plus 75 ; Greenhill Country Club: upper C equals 1,000 s plus 65 Regal Hotel: C=1,000s+75; Greenhill Country Club: C=500s+65 Regal Hotel: upper C equals 1,000 s plus 75 ; Greenhill Country Club: upper C equals 500 s plus 65 Regal Hotel: C=75s+500; Greenhill Country Club: C=65s+1,000 Regal Hotel: upper C equals 75 s plus 500 ; Greenhill Country Club: upper C equals 65 s plus 1,000 Regal Hotel: C=75s+1,000; Greenhill Country Club: C=65s+500

Answer 1

To create a pair of linear equations that represent the costs for both venues, we start with the given information:

1. Regal Hotel:

   • Ballroom rental fee: $500
   • Cost per student: $75
   • Total cost, \( C \), for \( s \) students is given by: \[ C = 500 + 75s \]

2. Greenhill Country Club:

   • Ballroom rental fee: $1,000
   • Cost per student: $65
   • Total cost, \( C \), for \( s \) students is given by: \[ C = 1,000 + 65s \]

Thus, the pair of linear equations representing this real-world problem is:

• Regal Hotel: \( C = 500 + 75s \)
• Greenhill Country Club: \( C = 1,000 + 65s \)

Among the response options provided, the one that matches this correct formulation is:

Regal Hotel: C = 500 + 75s; Greenhill Country Club: C = 1,000 + 65s (though not listed exactly in your options).

If we reformat it with \( C \) first instead of \( s \):

• Regal Hotel: \( C = 75s + 500 \)
• Greenhill Country Club: \( C = 65s + 1,000 \)

This also matches the option that says:

• Regal Hotel: \( C = 75s + 500 \); Greenhill Country Club: \( C = 65s + 1,000 \)

Although the options you provided have different variable placements, it's important to ensure we align to the required structure.

So, the best final answer based on readability is:

Regal Hotel: C = 75s + 500; Greenhill Country Club: C = 65s + 1,000.