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.
Regal Hotel: C=75s+1,000; Greenhill Country Club: C=65s+500
Regal Hotel: C=500s+75; Greenhill Country Club: C=1,000s+65
Regal Hotel: C=1,000s+75; Greenhill Country Club: C=500s+65
Regal Hotel: C=75s+500; Greenhill Country Club: C=65s+1,000
The correct pair of linear equations that represent this real-world problem is:
Regal Hotel: C = 75s + 500
Greenhill Country Club: C = 65s + 1,000
The correct pair of linear equations that represent this real-world problem is:
Regal Hotel: C = 75s + 500
Greenhill Country Club: C = 65s + 1,000
The correct pair of linear equations that represent this real-world problem is:
Regal Hotel: C = 75s + 500
Greenhill Country Club: C = 65s + 1,000
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.
b+c=12,500; 5b+10c=2,000
b+c=2,000; 5b+10c=12,500
b+c=2,000; 10b+5c=12,500
b+c=12,500; 10b+5c=2,000
The correct pair of linear equations that represent this situation is:
b + c = 2,000
10b + 5c = 12,500
Solve this real-world problem using a system of equations. The O’Donnells are having a birthday party for their son, and they plan to have a clown bring balloons to the party. Balloon Express charges $2 per balloon and $10 for delivery. Balloon Mania charges $1.50 per balloon and $20 for delivery. If the O’Donnells plan to order 30 balloons, which company should they choose, and how much will they save?
Balloon Mania; $25
Balloon Express; $25
Balloon Mania; $5
Balloon Express; $5
To solve this problem using a system of equations, let's set up the equations for each company:
Let x be the number of balloons being ordered.
For Balloon Express, the cost equation is:
C1 = 2x + 10
For Balloon Mania, the cost equation is:
C2 = 1.50x + 20
Given that x = 30 (the O'Donnells plan to order 30 balloons), we can substitute this value into each equation:
C1 = 2(30) + 10 = 60 + 10 = 70
C2 = 1.50(30) + 20 = 45 + 20 = 65
Therefore, the O'Donnells should choose Balloon Mania, as it will cost them $65. They will save $5 by choosing Balloon Mania over Balloon Express.
The Spanish Club at Santa Fe Middle School wants to sell mini quiches to raise money for a field trip. The culinary department at their school will make the quiches for $30 plus $0.50 per quiche for the ingredients. The Spanish Club wants to sell each quiche for $2. How many quiches will they need to sell in order to break even?
45 quiches
20 quiches
75 quiches
12 quiches
To find how many quiches the Spanish Club needs to sell in order to break even, we need to set up the equation:
Let q be the number of quiches to be sold.
The cost equation for the culinary department making the quiches is:
C1 = 30 + 0.50q
The revenue equation for the Spanish Club selling the quiches is:
C2 = 2q
To break even, the cost C1 should be equal to the revenue C2, so we can set up the equation:
30 + 0.50q = 2q
Simplifying the equation, we have:
0.50q = 30
q = 60
Therefore, the Spanish Club needs to sell 60 quiches in order to break even.