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)ResponsesBalloon Mania; $5Balloon Mania; $5Balloon Express; $5 Balloon Express; $5 Balloon Mania; $25 Balloon Mania; $25 Balloon Express; $25

1 answer

To find out which company the O'Donnells should choose, we can set up equations for the total cost from each company based on their pricing structures.

Let \( x \) be the number of balloons ordered, which is given as 30.

For Balloon Express:

  • Cost per balloon: $2
  • Delivery fee: $10

The total cost can be calculated with the equation: \[ \text{Total Cost}_{\text{Balloon Express}} = 2x + 10 \]

Substituting \( x = 30 \): \[ \text{Total Cost}_{\text{Balloon Express}} = 2(30) + 10 = 60 + 10 = 70 \]

For Balloon Mania:

  • Cost per balloon: $1.50
  • Delivery fee: $20

The total cost can be calculated with the equation: \[ \text{Total Cost}_{\text{Balloon Mania}} = 1.5x + 20 \]

Substituting \( x = 30 \): \[ \text{Total Cost}_{\text{Balloon Mania}} = 1.5(30) + 20 = 45 + 20 = 65 \]

Now, let's compare the total costs:

  • Total cost from Balloon Express: $70
  • Total cost from Balloon Mania: $65

Conclusion:

The O'Donnells should choose Balloon Mania since their total cost is less. The savings can be calculated as follows: \[ \text{Savings} = \text{Total Cost}{\text{Balloon Express}} - \text{Total Cost}{\text{Balloon Mania}} = 70 - 65 = 5 \]

Thus, the O'Donnells should choose Balloon Mania; $5 savings.