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)

Question

Responses

Balloon Mania; $5
Balloon Mania; $5

Balloon Express; $5
Balloon Express; $5

Balloon Express; $25
Balloon Express; $25

Balloon Mania; $25 

Answer 1

Let's set up the equations based on the costs of ordering balloons from both companies.

For Balloon Express:

• Cost per balloon: $2
• Delivery fee: $10
• Total cost formula: \[ C_{Express} = 2x + 10 \] Where \(x\) is the number of balloons.

For Balloon Mania:

• Cost per balloon: $1.50
• Delivery fee: $20
• Total cost formula: \[ C_{Mania} = 1.5x + 20 \]

Since the O’Donnells plan to order 30 balloons (\(x = 30\)), we can substitute this value into the cost equations for both companies.

Calculating for Balloon Express: \[ C_{Express} = 2(30) + 10 = 60 + 10 = 70 \]

Calculating for Balloon Mania: \[ C_{Mania} = 1.5(30) + 20 = 45 + 20 = 65 \]

Comparing the total costs:

• Cost from Balloon Express: $70
• Cost from Balloon Mania: $65

Calculating the Savings: \[ \text{Savings} = C_{Express} - C_{Mania} = 70 - 65 = 5 \]

So, the O’Donnells should choose Balloon Mania, and they will save $5.

The correct response is: Balloon Mania; $5.