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?
Responses
Balloon Mania; $5
Balloon Mania; $25
Balloon Express; $25
Balloon Express; $5
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
The total cost for Balloon Mania is: 1.5y + 20
Since the O’Donnells plan to order a total of 30 balloons, we know that x + y = 30
We can write a system of equations:
2x + 10 = 1.5y + 20
x + y = 30
Solving the system of equations:
2x + 10 = 1.5y + 20
2x = 1.5y + 10
x = 0.75y + 5
Substitute x = 30 - y into x = 0.75y + 5:
30 - y = 0.75y + 5
25 = 1.75y
y = 14.29 (rounded to the nearest whole number, y = 14)
From x + y = 30:
x + 14 = 30
x = 16
Now, calculate the total cost for each option:
For Balloon Express: 2(16) + 10 = $42
For Balloon Mania: 1.5(14) + 20 = $41
The O'Donnells should choose Balloon Mania. They will save $1 by choosing Balloon Mania instead of Balloon Express.
Therefore, the correct response is:
Balloon Mania; $1