Solve this real world problem using a system of equations. The O’Donnell’s are having a birthday party for their son and they plan 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’s plan to order 30 balloons, which company should they choose and how many will they have.
Let's denote the number of balloons the O'Donnell's order from Balloon Express as "b1" and the number of balloons they order from Balloon Mania as "b2".
According to the given information, Balloon Express charges $2 per balloon and $10 for delivery, while Balloon Mania charges $1.50 per balloon and $20 for delivery.
We can set up the following system of equations to represent the total cost for each company:
Total cost for Balloon Express: 2b1 + 10
Total cost for Balloon Mania: 1.50b2 + 20
The O'Donnell's plan to order 30 balloons in total, so we can also set up the following equation to represent the total number of balloons:
Total number of balloons: b1 + b2 = 30
To determine which company they should choose and how many balloons they will have, we need to solve this system of equations.
Substitute the equation for b1 + b2 into the equations for the total cost of each company:
Total cost for Balloon Express: 2(30 - b2) + 10 = 60 - 2b2 + 10 = 70 - 2b2
Total cost for Balloon Mania: 1.50b2 + 20
Set the two total cost equations equal to each other and solve for b2:
70 - 2b2 = 1.50b2 + 20
-2b2 - 1.50b2 = 20 - 70
-3.5b2 = -50
b2 = -50 / -3.5
b2 = 14.29 (approx.)
Since we cannot have a fraction of a balloon, we round b2 to the nearest whole number, which is 14.
Now that we know b2, we can substitute it into the equation for the total number of balloons to find b1:
b1 + 14 = 30
b1 = 30 - 14
b1 = 16
Therefore, the O'Donnell's should choose Balloon Mania and order 14 balloons, and they will have a total of 16 balloons.