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
Balloon Express; $25
Balloon Express; $25
Balloon Mania; $25
Balloon Mania; $25
Balloon Express; $5
Balloon Express; $5
Balloon Mania; $5
Let's create a system of equations to represent the total cost for each company:
Let x be the number of balloons ordered from Balloon Express, and y be the number of balloons ordered from Balloon Mania.
For Balloon Express:
Total cost = $2x + $10 (delivery)
For Balloon Mania:
Total cost = $1.50y + $20 (delivery)
Given that the O'Donnells plan to order 30 balloons, we can set up the following system of equations:
x + y = 30
2x + 10 = 1.50y + 20
Solving the system of equations:
From the first equation:
x = 30 - y
Substitute x into the second equation:
2(30 - y) + 10 = 1.50y + 20
60 - 2y + 10 = 1.50y + 20
70 - 10 = 1.5y + 20
60 = 1.5y
y = 40
Substitute y back into x = 30 - y:
x = 30 - 40
x = 10
Therefore, Balloon Express would charge $2(10) + $10 = $30, while Balloon Mania would charge $1.50(40) + $20 = $80. The O'Donnells should choose Balloon Express because they would save $80 - $30 = $50.
The correct response is: Balloon Express; $50.