The correct pair of linear equations that model this situation is:
b+c=2,000; 5b+10c=12,500
Question
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 plus c equals 2,000 ; 10 b plus 5 c equals 12,500
9 answers
Question
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 Mania; $5
Balloon Mania; $5
Balloon Express; $5
Balloon Express; $5
Balloon Express; $25
Balloon Express; $25
Balloon Mania; $25
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 Mania; $5
Balloon Mania; $5
Balloon Express; $5
Balloon Express; $5
Balloon Express; $25
Balloon Express; $25
Balloon Mania; $25
To solve this problem, we can set up a system of equations.
Let x represent the number of balloons the O'Donnells order and y represent the cost.
For Balloon Express, the cost y would be:
y = 2x + 10
For Balloon Mania, the cost y would be:
y = 1.50x + 20
Since the O'Donnells plan to order 30 balloons, we can substitute x = 30 into the equations to find the costs.
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.
Let x represent the number of balloons the O'Donnells order and y represent the cost.
For Balloon Express, the cost y would be:
y = 2x + 10
For Balloon Mania, the cost y would be:
y = 1.50x + 20
Since the O'Donnells plan to order 30 balloons, we can substitute x = 30 into the equations to find the costs.
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.
so its the first response
Yes, that's correct. The correct response is:
Balloon Mania; $5
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
12 quiches
12 quiches
45 quiches
45 quiches
20 quiches
20 quiches
75 quiches
75 quiches
Responses
12 quiches
12 quiches
45 quiches
45 quiches
20 quiches
20 quiches
75 quiches
75 quiches
To determine the number of quiches they need to sell in order to break even, we can set up a linear equation.
Let x represent the number of quiches they need to sell. The cost will be equal to the revenue they generate.
The cost for making the quiches is $30 plus $0.50 per quiche, so the cost equation is:
Cost = $30 + $0.50x
The selling price per quiche is $2, so the revenue equation is:
Revenue = $2x
To break even, the cost must equal the revenue:
$30 + $0.50x = $2x
To solve this equation, we can subtract $0.50x from both sides:
$30 = $1.50x
Now, we can divide both sides by $1.50 to solve for x:
$x = $30 / $1.50
x = 20
Therefore, the Spanish Club will need to sell 20 quiches in order to break even.
The correct response is:
20 quiches
Let x represent the number of quiches they need to sell. The cost will be equal to the revenue they generate.
The cost for making the quiches is $30 plus $0.50 per quiche, so the cost equation is:
Cost = $30 + $0.50x
The selling price per quiche is $2, so the revenue equation is:
Revenue = $2x
To break even, the cost must equal the revenue:
$30 + $0.50x = $2x
To solve this equation, we can subtract $0.50x from both sides:
$30 = $1.50x
Now, we can divide both sides by $1.50 to solve for x:
$x = $30 / $1.50
x = 20
Therefore, the Spanish Club will need to sell 20 quiches in order to break even.
The correct response is:
20 quiches
Question
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
50 hot dogs and 250 pretzels
50 hot dogs and 250 pretzels
200 hot dogs and 100 pretzels
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
50 hot dogs and 250 pretzels
50 hot dogs and 250 pretzels
200 hot dogs and 100 pretzels
To solve this problem, we can set up a system of equations.
Let h represent the number of hot dogs sold and p represent the number of pretzels sold.
The income from selling hot dogs would be:
Income from hot dogs = $4 * h
The income from selling pretzels would be:
Income from pretzels = $2 * p
We are given that they want to earn an income of $800, so we can set up the following equation:
Income from hot dogs + Income from pretzels = $800
Substituting the equations for the income from hot dogs and pretzels, we get:
$4h + $2p = $800
We also know that they have a total of 300 hot dogs and pretzels in stock:
h + p = 300
To solve this system of equations, we can use substitution or elimination. Here, we will use elimination.
Multiply the second equation by 2 to eliminate the p term:
2h + 2p = 600
Subtract this equation from the first equation:
$4h - 2h = $800 - $600
$2h = $200
h = 100
Substitute h = 100 into the second equation to solve for p:
100 + p = 300
p = 200
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
Let h represent the number of hot dogs sold and p represent the number of pretzels sold.
The income from selling hot dogs would be:
Income from hot dogs = $4 * h
The income from selling pretzels would be:
Income from pretzels = $2 * p
We are given that they want to earn an income of $800, so we can set up the following equation:
Income from hot dogs + Income from pretzels = $800
Substituting the equations for the income from hot dogs and pretzels, we get:
$4h + $2p = $800
We also know that they have a total of 300 hot dogs and pretzels in stock:
h + p = 300
To solve this system of equations, we can use substitution or elimination. Here, we will use elimination.
Multiply the second equation by 2 to eliminate the p term:
2h + 2p = 600
Subtract this equation from the first equation:
$4h - 2h = $800 - $600
$2h = $200
h = 100
Substitute h = 100 into the second equation to solve for p:
100 + p = 300
p = 200
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
7 answers