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.
A. Regal Hotel: C=500s+75; Greenhill Country Club: C=1,000s+65
B. Regal Hotel: C=75s+1,000; Greenhill Country Club: C=65s+500
C. Regal Hotel: C=1,000s+75; Greenhill Country Club: C=500s+65
D. Regal Hotel: C=75s+500; Greenhill Country Club: C=65s+1,000
A. Regal Hotel: C=500s+75; Greenhill Country Club: C=1,000s+65
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.
A. b+c=2,000; 5b+10c=12,500
B. b+c=2,000; 10b+5c=12,500
C. b+c=12,500; 10b+5c=2,000
D. b+c=12,500; 5b+10c=2,000
B. 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?
A. Balloon Mania; $25
B. Balloon Express; $5
C. Balloon Mania; $5
D. Balloon Express; $25
Let's use a system of equations to solve this problem.
Let x be the number of balloons and y be the total cost.
For Balloon Express:
y = 2x + 10
For Balloon Mania:
y = 1.50x + 20
Given that the O'Donnells plan to order 30 balloons:
Substitute x = 30 into the equations above:
For Balloon Express:
y = 2(30) + 10
y = 60 + 10
y = 70
For Balloon Mania:
y = 1.50(30) + 20
y = 45 + 20
y = 65
Therefore, the O'Donnells should choose Balloon Mania, and they will save $5 compared to Balloon Express.
The correct answer is:
C. Balloon Mania; $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?
A. 75 quiches
B. 20 quiches
C. 12 quiches
D. 45 quiches
Let's set up the equation for the cost and revenue:
Let q be the number of quiches. The cost equation is given by: Cost = $30 + $0.50q
The revenue equation is: Revenue = $2q
To break even, the cost equals the revenue, so:
$30 + $0.50q = $2q
$30 = $1.50q
q = 30 / 1.50
q = 20
Therefore, they need to sell 20 quiches in order to break even.
The correct answer is:
B. 20 quiches
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?
A. 200 hot dogs and 100 pretzels
B. 50 hot dogs and 250 pretzels
C. 100 hot dogs and 200 pretzels
D. 250 hot dogs and 50 pretzels
Let's set up a system of equations to solve this problem.
Let h be the number of hot dogs and p be the number of pretzels.
Given:
h + p = 300 (total number of hot dogs and pretzels)
4h + 2p = 800 (income goal)
Solving the first equation for h:
h = 300 - p
Substitute h = 300 - p into the second equation:
4(300 - p) + 2p = 800
1200 - 4p + 2p = 800
-2p = -400
p = 200
Substitute the value of p back into the first equation to find h:
h + 200 = 300
h = 100
Therefore, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.
The correct answer is:
C. 100 hot dogs and 200 pretzels