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; $25 Balloon Express; $25 Balloon Mania; $25 Balloon Mania; $25 Balloon Express; $5
Let's represent the number of balloons as x.
For Balloon Express, the total cost would be 2x + 10.
For Balloon Mania, the total cost would be 1.50x + 20.
We are given that the O'Donnells plan to order 30 balloons, so x = 30.
For Balloon Express, the total cost would be 2(30) + 10 = 70.
For Balloon Mania, the total cost would be 1.50(30) + 20 = 65.
Therefore, the O'Donnells should choose Balloon Mania, and they would save $5.
Let's solve the problem step-by-step using a system of equations.
Let's assume the number of balloons ordered is represented by 'x'.
For Balloon Express, each balloon costs $2 and there is a $10 delivery charge. So the total cost for Balloon Express can be represented by the equation: 2x + 10.
For Balloon Mania, each balloon costs $1.50 and there is a $20 delivery charge. So the total cost for Balloon Mania can be represented by the equation: 1.50x + 20.
Since the O'Donnells plan to order 30 balloons, we can substitute x = 30 into the equations.
For Balloon Express: 2(30) + 10 = 60 + 10 = 70.
For Balloon Mania: 1.50(30) + 20 = 45 + 20 = 65.
From the calculations, we can see that the O'Donnells should choose Balloon Mania.
To find out how much they will save, we subtract the total cost of Balloon Mania from the total cost of Balloon Express: 70 - 65 = $5.
Therefore, the O'Donnells should choose Balloon Mania and they will save $5.
So the correct response is: Balloon Mania; $5.
To solve this real-world problem using a system of equations, we need to define variables for the number of balloons ordered from each company.
Let's say x represents the number of balloons ordered from Balloon Express, and y represents the number of balloons ordered from Balloon Mania.
Based on the information given, we can set up the following equations:
Equation 1: 2x + 10 = total cost from Balloon Express
Equation 2: 1.50y + 20 = total cost from Balloon Mania
Equation 3: x + y = 30 (since the O'Donnells plan to order a total of 30 balloons)
Now, we can solve this system of equations to find the answer.
First, let's rearrange Equation 3 to solve for x:
x = 30 - y
Substituting this expression for x into Equation 1:
2(30 - y) + 10 = total cost from Balloon Express
Simplifying:
60 - 2y + 10 = total cost from Balloon Express
70 - 2y = total cost from Balloon Express
Using Equation 2, we know that:
1.50y + 20 = total cost from Balloon Mania
Now, we can compare the total costs from both companies to determine which company the O'Donnells should choose.
We have:
70 - 2y = 1.50y + 20
-2y - 1.50y = 20 - 70
-3.50y = -50
y = -50 / -3.50
y ≈ 14.29
Since y represents the number of balloons ordered from Balloon Mania, it should be a whole number. We can't order fractional balloons, so let's round it down to 14.
Using Equation 3, we can find the value of x:
x = 30 - y
x = 30 - 14
x = 16
So, the O'Donnells should choose to order 16 balloons from Balloon Express and 14 balloons from Balloon Mania.
Now, let's calculate the total costs from each company:
Total cost from Balloon Express = 2x + 10
Total cost from Balloon Mania = 1.50y + 20
Total cost from Balloon Express = 2(16) + 10 = 42
Total cost from Balloon Mania = 1.50(14) + 20 = 41
Therefore, the O'Donnells should choose Balloon Mania, and they will save $1 compared to Balloon Express. The correct response 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 45 quiches 45 quiches 75 quiches 75 quiches 12 quiches
Let's represent the number of quiches as x.
The cost to make the quiches would be $30 + $0.50x.
The revenue from selling the quiches would be $2x.
To break even, the revenue should equal the cost:
$2x = $30 + $0.50x
Simplifying the equation:
$2x - $0.50x = $30
$1.50x = $30
Dividing both sides of the equation by $1.50:
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."
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 100 hot dogs and 200 pretzels 100 hot dogs and 200 pretzels 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
Let's represent the number of hot dogs as x and the number of pretzels as y.
The income from selling hot dogs can be represented as $4x.
The income from selling pretzels can be represented as $2y.
We are given that the boosters want to earn a total income of $800, so we can set up the following equation:
$4x + $2y = $800
We also know that there are 300 hot dogs and pretzels in stock, so:
x + y = 300
Now we have a system of equations:
$4x + $2y = $800
x + y = 300
To solve this system, we can use the substitution method.
Solve the second equation for x: x = 300 - y
Substitute this value of x into the first equation:
$4(300 - y) + $2y = $800
1200 - 4y + 2y = $800
-2y = $800 - $1200
-2y = -$400
y = -$400 / -2
y = 200
Now substitute the value of y into the second equation to find x:
x + 200 = 300
x = 300 - 200
x = 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."