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=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=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=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=75s+1,000; Greenhill Country Club: C=65s+500
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.(1 point)
Responses
b+c=2,000; 10b+5c=12,500
b plus c equals 2,000 ; 10 b plus 5 c equals 12,500
b+c=2,000; 5b+10c=12,500
b plus c equals 2,000 ; 10 b plus 10 c equals 12,500
b+c=12,500; 5b+10c=2,000
b plus c equals 12,500 ; 5 b plus 10 c equals 2,000
b+c=12,500; 10b+5c=2,000
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?(1 point)
Responses
Balloon Express; $5
Balloon Express; $5
Balloon Express; $25
Balloon Express; $25
Balloon Mania; $5
Balloon Mania; $5
Balloon Mania; $25
Balloon Mania; $5
Let's represent the cost for Balloon Express and Balloon Mania using a system of equations. Let's denote the cost for Balloon Express as E and the cost for Balloon Mania as M.
For Balloon Express:
E = 2(30) + 10 = 60 + 10 = 70
For Balloon Mania:
M = 1.5(30) + 20 = 45 + 20 = 65
Therefore, the O’Donnells should choose Balloon Mania as it is cheaper. They will save $70 - $65 = $5.
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?(1 point)
Responses
20 quiches
20 quiches
75 quiches
75 quiches
45 quiches
45 quiches
12 quiches
The cost to make each quiche is $30 (fixed cost) + $0.50 per quiche (variable cost). The revenue from selling each quiche is $2. To break even, the total cost must equal the total revenue.
Let q be the number of quiches sold.
Cost = 30 + 0.50q
Revenue = 2q
To break even: 30 + 0.50q = 2q
Solving for q:
30 = 2q - 0.50q
30 = 1.50q
q = 30 / 1.50
q = 20
Therefore, the Spanish Club at Santa Fe Middle School will need to sell 20 quiches in order to break even.
The Baynard High School Boosters are selling hot dogs and pretzels at the concession stand. They have 300 hot dogs and pretzels in stock and want to earn an income of $800. They plan to sell the hot dogs for $4 each and the pretzels for $2 each. How many hot dogs and how many pretzels do the boosters need to sell to reach their goal of $800?(1 point)
Responses
250 hot dogs and 50 pretzels
250 hot dogs and 50 pretzels
100 hot dogs and 200 pretzels
100 hot dogs and 200 pretzels
200 hot dogs and 100 pretzels
200 hot dogs and 100 pretzels
50 hot dogs and 250 pretzels
Let's represent the number of hot dogs as H and the number of pretzels as P.
The total income is given by:
Total Income = 4H + 2P
The boosters want to earn an income of $800:
4H + 2P = 800
Since they have 300 hot dogs and pretzels in stock:
H + P = 300
We have a system of equations:
4H + 2P = 800
H + P = 300
Let's solve this system of equations to find the values of H and P.
From the second equation, we have:
H = 300 - P
Substitute this into the first equation:
4(300 - P) + 2P = 800
1200 - 4P + 2P = 800
-2P = -400
P = 200
Now substitute P = 200 back into H = 300 - P:
H = 300 - 200 = 100
Therefore, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.
The correct response is: 100 hot dogs and 200 pretzels.