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)

Balloon Express; $5 Balloon Express; $5 Balloon Mania; $25 Balloon Mania; $25 Balloon Mania; $5 Balloon Mania; $5 Balloon Express; $25

1 answer

To determine which company the O'Donnells should choose for their balloons, we can set up equations for the total cost from each company.

Let \( x \) be the number of balloons ordered, which is 30 in this case.

For Balloon Express:

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

The total cost (TE) for Balloon Express can be calculated as: \[ TE_{\text{Express}} = 2x + 10 \] Substituting \( x = 30 \): \[ TE_{\text{Express}} = 2(30) + 10 = 60 + 10 = 70 \]

For Balloon Mania:

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

The total cost for Balloon Mania can be calculated as: \[ TE_{\text{Mania}} = 1.5x + 20 \] Substituting \( x = 30 \): \[ TE_{\text{Mania}} = 1.5(30) + 20 = 45 + 20 = 65 \]

Summary of Costs:

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

Decision:

The O'Donnells should choose Balloon Mania, as it costs $65, which is cheaper than Balloon Express by: \[ 70 - 65 = 5 \]

Conclusion:

The O'Donnells should choose Balloon Mania; $5 saved compared to Balloon Express.