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 Mania; $5
Balloon Mania; $5

Balloon Mania; $25 
Balloon Mania; $25 

Balloon Express; $25
Balloon Express; $25

Balloon Express; $5
Balloon Express; $5

1 answer

Let's set up the cost equations for both companies based on the prices provided.

Balloon Express:

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

If the O'Donnells order 30 balloons, the total cost \( C_E \) for Balloon Express can be calculated as follows: \[ C_E = (2 \times 30) + 10 = 60 + 10 = 70 \]

Balloon Mania:

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

The total cost \( C_M \) for Balloon Mania is: \[ C_M = (1.5 \times 30) + 20 = 45 + 20 = 65 \]

Now we can compare the total costs:

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

To find out which company the O'Donnells should choose, we can identify the savings by subtracting the costs: \[ \text{Savings} = C_E - C_M = 70 - 65 = 5 \]

Thus, the O'Donnells should choose Balloon Mania and they will save $5.

The correct response is: Balloon Mania; $5