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; 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 plus c equals 12,500 ; 10 b plus 5 c equals 2,000
b+c=2,000; 10b+5c=12,500
b+c=2,000; 5b+10c=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
Let's represent the number of balloons as "b" and the total cost as "c".
For Balloon Express, the cost is $2 per balloon and $10 for delivery, so the equation would be:
c = 2b + 10
For Balloon Mania, the cost is $1.50 per balloon and $20 for delivery, so the equation would be:
c = 1.5b + 20
Since the O'Donnells plan to order 30 balloons, we can substitute b = 30 into both equations:
For Balloon Express: c = 2(30) + 10 = 60 + 10 = 70
For Balloon Mania: c = 1.5(30) + 20 = 45 + 20 = 65
Therefore, the O'Donnells should choose Balloon Mania, and they would save $5.
Correct response:
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
75 quiches
75 quiches
12 quiches
12 quiches
20 quiches
20 quiches
45 quiches
Let's represent the number of quiches as "q" and the total cost as "C".
The cost of making the quiches is $30 plus $0.50 per quiche, so the cost equation is:
C = 30 + 0.50q
The revenue from selling the quiches is $2 per quiche, so the revenue equation is:
R = 2q
In order to break even, the total cost and total revenue should be equal:
30 + 0.50q = 2q
30 = 2q - 0.50q
30 = 1.5q
q = 30 / 1.5
q = 20
Therefore, the Spanish Club will need to sell 20 quiches in order to break even.
Correct response:
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
200 hot dogs and 100 pretzels
200 hot dogs and 100 pretzels
100 hot dogs and 200 pretzels
Let's represent the number of hot dogs as "h", the number of pretzels as "p", and the total income as "I".
The total income earned from selling hot dogs and pretzels is given by the equation:
I = 4h + 2p
From the information provided, we know that the boosters want to earn an income of $800, so we have:
800 = 4h + 2p
The boosters have 300 hot dogs and pretzels in stock, which gives us another equation:
h + p = 300
To solve for the number of hot dogs and pretzels needed to reach the goal of $800, we can simultaneously solve the two equations:
4h + 2p = 800
h + p = 300
Solving these equations, we find that h = 200 and p = 100
Therefore, the boosters need to sell 200 hot dogs and 100 pretzels to reach their goal of $800.
Correct Response:
200 hot dogs and 100 pretzels
so what are all the answer
1. For the Jackson Jammers giving away bags and caps at their next game:
b+c=2,000; 5b+10c=12,500
Answer: b plus c equals 2,000 ; 5 b plus 10 c equals 12,500
2. The O'Donnells deciding between Balloon Express and Balloon Mania:
Balloon Mania; $5
3. The Spanish Club at Santa Fe Middle School selling mini quiches:
20 quiches
4. The Baynard High School Boosters selling hot dogs and pretzels:
200 hot dogs and 100 pretzels