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?

Question

A: Balloon Express $25
B: Balloon Express $5
C: Balloon Mania $25
D: Balloon Mania $5

Answer 1

Let's set up a system of equations to represent the total cost for each company:

Let x be the number of balloons ordered from Balloon Express
Let y be the number of balloons ordered from Balloon Mania

For Balloon Express:
Total cost = 2x + 10

For Balloon Mania:
Total cost = 1.5y + 20

Given:
x + y = 30

Now we can substitute x = 30 - y into the equations for both companies:

For Balloon Express:
Total cost = 2(30 - y) + 10
Total cost = 60 - 2y + 10
Total cost = 70 - 2y

For Balloon Mania:
Total cost = 1.5y + 20

Now we can set the two total costs equal to each other to find out when they are the same:

70 - 2y = 1.5y + 20
50 = 3.5y
y = 14.2857

Since you cannot order a fraction of a balloon, you would order 14 balloons from Balloon Mania and 16 balloons from Balloon Express.

Total cost for Balloon Express: 2(16) + 10 = $42
Total cost for Balloon Mania: 1.5(14) + 20 = $41

Therefore, the O'Donnells should choose Balloon Mania, and they would save $1.