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; 10b+5c=2,000
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=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; $25
Balloon Mania; $5
Balloon Express; $5
Balloon Mania; $25
Let's denote the number of balloons as 'b'.
For Balloon Express: Cost = $2b + $10
For Balloon Mania: Cost = $1.5b + $20
Given that they are ordering 30 balloons, we can set up the system of equations:
2b + 10 = 30
1.5b + 20 = 30
Solving the first equation:
2b + 10 = 30
2b = 20
b = 10
Using b = 10 in the second equation:
1.5(10) + 20 = 30
15 + 20 = 30
35 = 30
Therefore, Balloon Express does not meet the requirements. The O'Donnells should choose Balloon Mania which costs $25. They would save $5 by choosing Balloon Mania.
So, the answer is: 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?(1 point)
Responses
20 quiches
20 quiches
75 quiches
75 quiches
12 quiches
12 quiches
45 quiches
Let's denote the cost of making the quiches as 'C'.
C = $30 + $0.50 * number of quiches (q)
The Spanish Club wants to sell each quiche for $2, so the revenue from selling q quiches would be 2q.
The break-even point occurs when the revenue equals the cost, so:
2q = 30 + 0.5q
Solving for q:
2q = 30 + 0.5q
1.5q = 30
q = 20
Therefore, the Spanish Club will need to sell 20 quiches in order to break even.
So, the answer is: 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?(1 point)
Responses
50 hot dogs and 250 pretzels
50 hot dogs and 250 pretzels
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
Let's define the number of hot dogs as 'h' and the number of pretzels as 'p'.
Given:
h + p = 300 (they have 300 hot dogs and pretzels in stock)
4h + 2p = 800 (they want to earn an income of $800)
Using these two equations, we can solve for the values of h and p:
Multiply the first equation by 2 to eliminate p:
2h + 2p = 600
Subtract the first equation from the second equation:
2h + 2p - (h + p) = 600 - 300
h = 300
Substitute the value of h back into the first equation:
300 + p = 300
p = 0
Therefore, the only way for them to reach their goal of $800 is to sell 300 hot dogs (h) and 0 pretzels (p).
So, the answer is: 300 hot dogs and 0 pretzels.
they have to sell the same number hot dogs and pretzel so it can no be 300 hot dogs and 0 pretzels.
You are correct, I apologize for the oversight. Since they have to sell the same number of hot dogs and pretzels to reach the goal of $800, let's use the equations:
h = number of hot dogs
p = number of pretzels
h = p
h + p = 300
4h + 2p = 800
Substitute h = p into the second equation:
2h = 300
h = 150
Then:
150 + p = 300
p = 150
Therefore, the Boosters need to sell 150 hot dogs and 150 pretzels to reach their goal of $800.
The correct answer is: 150 hot dogs and 150 pretzels.