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
what is the answer
To solve this problem using a system of equations, we can represent the cost of balloons from Balloon Express as "BE" and the cost of balloons from Balloon Mania as "BM".
According to the information given, Balloon Express charges $2 per balloon and $10 for delivery, so we can write the equation for Balloon Express as:
BE = 2(30) + 10
Balloon Mania charges $1.50 per balloon and $20 for delivery, so we can write the equation for Balloon Mania as:
BM = 1.50(30) + 20
By calculating these equations, we find that BE = 60 + 10 = $70 and BM = 1.50(30) + 20 = $65.
Therefore, the O'Donnells should choose Balloon Mania because they will save $5 compared to Balloon Express.
To solve this problem using a system of equations, let's denote the number of balloons as 'x'.
For Balloon Express, the total cost can be calculated as:
Cost of balloons = 2x
Delivery cost = 10
So the total cost for Balloon Express is: 2x + 10
For Balloon Mania, the total cost can be calculated as:
Cost of balloons = 1.5x
Delivery cost = 20
So the total cost for Balloon Mania is: 1.5x + 20
Since the O'Donnells plan to order 30 balloons (x = 30), we can calculate the total cost for each company:
Balloon Express: 2(30) + 10 = 60 + 10 = $70
Balloon Mania: 1.5(30) + 20 = 45 + 20 = $65
Therefore, the O'Donnells should choose Balloon Mania since it has the lower cost. They will save $70 - $65 = $5 by choosing Balloon Mania.
So the answer is: Balloon Mania; $5.
To solve this real-world problem using a system of equations, we can set up two equations representing the total cost for each company.
Let's assume that x represents the number of balloons ordered from Balloon Express and y represents the number of balloons ordered from Balloon Mania.
For Balloon Express:
Total cost = (cost per balloon) * (number of balloons) + (delivery cost)
We are given that Balloon Express charges $2 per balloon and $10 for delivery, so the equation for Balloon Express becomes:
2x + 10
For Balloon Mania:
Total cost = (cost per balloon) * (number of balloons) + (delivery cost)
We are given that Balloon Mania charges $1.50 per balloon and $20 for delivery, so the equation for Balloon Mania becomes:
1.50y + 20
We know that the O'Donnells plan to order a total of 30 balloons, so we can combine the equations and set them equal to 30:
x + y = 30
Now, we can solve this system of equations to find the values of x and y. By substitution or elimination, we get:
x + y = 30
From the first equation, we get:
x = 30 - y
Now, substitute the value of x in the equation for Balloon Express:
2(30 - y) + 10 = 1.50y + 20
Simplify and solve for y:
60 - 2y + 10 = 1.50y + 20
70 - 10 = 1.50y + 2y
60 = 3.50y
Divide both sides by 3.50 to solve for y:
y = 60 / 3.50
y ≈ 17.14
Now, substitute the value of y in the equation x = 30 - y:
x = 30 - 17.14
x ≈ 12.86
So, the O'Donnells should choose Balloon Mania, as they will be saving money. Now, let's calculate how much they will save:
Cost from Balloon Express = 2x + 10 = 2(12.86) + 10 ≈ $36.72
Cost from Balloon Mania = 1.50y + 20 = 1.50(17.14) + 20 ≈ $46.71
The O'Donnells will save approximately $46.71 - $36.72 = $9.99 by choosing Balloon Mania.