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
Let's represent the cost of ordering from Balloon Express as E, and the cost of ordering from Balloon Mania as M.
Based on the given information, the cost from Balloon Express can be represented as: E = 2*(30) + 10 = 60 + 10 = 70
Similarly, the cost from Balloon Mania can be represented as: M = 1.50*(30) + 20 = 45 + 20 = 65
Therefore, the O'Donnells should choose Balloon Mania as it will cost them $65, while Balloon Express would cost $70.
By choosing Balloon Mania, the O'Donnells will save $70 - $65 = $5.
Let's represent the number of balloons ordered from Balloon Express as x, and the number of balloons ordered from Balloon Mania as y.
Based on the given information, we can set up the following system of equations:
Balloon Express:
Cost of balloons from Balloon Express = 2x
Cost of delivery from Balloon Express = 10
Balloon Mania:
Cost of balloons from Balloon Mania = 1.5y
Cost of delivery from Balloon Mania = 20
We know that the O'Donnells plan to order a total of 30 balloons, so we have the equation: x + y = 30
To determine which company they should choose, we need to compare the total cost from each company.
For Balloon Express, the total cost is: 2x + 10
For Balloon Mania, the total cost is: 1.5y + 20
To find out how much they will save, we need to calculate the difference between the two company's costs.
Substituting the value of x from the equation x + y = 30, we get:
2(30 - y) + 10 = 1.5y + 20
60 - 2y + 10 = 1.5y + 20
70 - 20 = 1.5y + 2y
50 = 3.5y
y = 14.29 (approximately)
Since the number of balloons must be a whole number, we can round up the value of y to 15.
Now, plugging the value of y back into x + y = 30, we can find the value of x:
x + 15 = 30
x = 30 - 15
x = 15
So, the O'Donnells should choose Balloon Express to save money.
To calculate how much they will save, we compare the total cost from both companies:
Total cost from Balloon Express: 2x + 10 = 2(15) + 10 = 30 + 10 = 40
Total cost from Balloon Mania: 1.5y + 20 = 1.5(15) + 20 = 22.5 + 20 = 42.5
Therefore, they will save $42.5 - $40 = $2.5 by choosing Balloon Express.
To solve this real-world problem, we can use a system of equations to compare the total costs of both companies. Let's assign variables to the unknown values in the problem.
Let's say the number of balloons ordered is "x" and the total cost for Balloon Express is "C1" and the total cost for Balloon Mania is "C2".
From the information given, we can set up the following equations:
For Balloon Express:
C1 = 2x + 10
For Balloon Mania:
C2 = 1.50x + 20
We know that the O'Donnells plan to order 30 balloons, so we substitute x = 30 into the equations:
For Balloon Express:
C1 = 2(30) + 10 = 60 + 10 = 70
For Balloon Mania:
C2 = 1.50(30) + 20 = 45 + 20 = 65
By comparing the total costs, we can see that the O'Donnells should choose Balloon Express since it will cost them $70, whereas Balloon Mania will cost them $65.
To determine the amount they will save, we subtract the total cost of Balloon Mania from Balloon Express:
Savings = C1 - C2 = 70 - 65 = $5
Therefore, the O'Donnells will save $5 by choosing Balloon Express over Balloon Mania.