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 Express; $5
Balloon Express; $5
Balloon Mania; $5
Balloon Mania; $5
Balloon Mania; $25
Let x be the number of balloons from Balloon Express and y be the number of balloons from Balloon Mania.
The total cost for Balloon Express is 2x + 10 and the total cost for Balloon Mania is 1.50y + 20.
Given that the total number of balloons is 30, we have the equation:
x + y = 30
Substitute x = 30 - y into the cost equations:
Cost for Balloon Express: 2(30 - y) + 10
Cost for Balloon Mania: 1.50y + 20
Now, set the two cost equations equal to each other and solve for y:
2(30 - y) + 10 = 1.50y + 20
60 - 2y + 10 = 1.50y + 20
70 - 2y = 1.50y + 20
50 = 3.50y
y = 14.29
Since you can't have a fraction of a balloon, round y up to 15 balloons from Balloon Mania.
Substitute y = 15 back into x + y = 30, we get:
x + 15 = 30
x = 15
Therefore, the O'Donnells should choose Balloon Mania, as they will save $5 compared to Balloon Express.