Solve the real world problem using a system of equations the o Donnell Are having a birthday party for their son and they are planning to have a clown bring balloons to the party balloon express charges two dollars per balloon and $10 for delivery balloon mania charges $1.50 per balloon and $20 for delivery if the O’Donnell plan to order 30 balloons, which company should they choose and how much will they save?
Let x be the number of balloons ordered from Balloon Express and y be the number of balloons ordered from Balloon Mania.
The total cost for Balloon Express is 2x + 10 and the total cost for Balloon Mania is 1.5y + 20.
Since the O'Donnell plan to order 30 balloons, we have the equation x + y = 30.
We can now set up a system of equations:
2x + 10 = 1.5y + 20
x + y = 30
We can solve this system of equations for x and y:
2x + 10 = 1.5(30 - x) + 20
2x + 10 = 45 - 1.5x + 20
2x + 10 = 65 - 1.5x
2x + 1.5x = 65 - 10
3.5x = 55
x = 15
Now that we have found x, we can find y:
x + y = 30
15 + y = 30
y = 15
Therefore, the O'Donnell should order 15 balloons from Balloon Express and 15 balloons from Balloon Mania.
The total cost for Balloon Express is 2(15) + 10 = $40
The total cost for Balloon Mania is 1.5(15) + 20 = $42.50
Therefore, the O'Donnell will save $2.50 by choosing Balloon Express.