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?
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 given by the equation:
2x + 10 = total cost
The total cost for Balloon Mania is given by the equation:
1.5y + 20 = total cost
Given that the total number of balloons ordered is 30:
x + y = 30
Now we can set up a system of equations to solve for x and y:
2x + 10 = 1.5(30-x) + 20
2x + 10 = 45 - 1.5x + 20
2x + 10 = 25 - 1.5x
3.5x = 15
x = 4.29
Since the number of balloons must be a whole number, the O'Donnells would order 4 balloons from Balloon Express and 26 balloons from Balloon Mania.
Comparing the total cost for each company:
Balloon Express: 2(4) + 10 = $18
Balloon Mania: 1.5(26) + 20 = $59
Therefore, the O'Donnells should choose Balloon Express, and they would save $41 by doing so.