Real-World Systems of Equations Quick Check

Question

3 of 53 of 5 Items
Question
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 Express; $5
Balloon Express; $5

Balloon Mania; $25 
Balloon Mania; $25 

Balloon Express; $25
Balloon Express; $25

Answer 1

To determine which company the O’Donnells should choose and how much they will save, we can set up equations based on the costs from each company.

1. Balloon Express:

   • Cost per balloon: $2
   • Delivery charge: $10
   • Total cost for 30 balloons = (cost per balloon × number of balloons) + delivery charge \[ C_{Express} = (2 \times 30) + 10 = 60 + 10 = 70 \]

2. Balloon Mania:

   • Cost per balloon: $1.50
   • Delivery charge: $20
   • Total cost for 30 balloons = (cost per balloon × number of balloons) + delivery charge \[ C_{Mania} = (1.50 \times 30) + 20 = 45 + 20 = 65 \]

Now that we have the total costs:

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

Next, we can find the savings: \[ \text{Savings} = C_{Express} - C_{Mania} = 70 - 65 = 5 \]

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

Answer: Balloon Mania; $5