Question

Solve this real-world problem using a system of equations. The O’Donell 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 Express; $25
Balloon Express; $25

Balloon Mania; $25 
Balloon Mania; $25 

Balloon Express; $5
Balloon Express; $5

Balloon Mania; $5

Answer 1

To determine which balloon service the O'Donnells should choose and how much they will save, we can set up equations to represent the total cost for each company based on the number of balloons they plan to order (30 balloons).

**For Balloon Express:**

- Price per balloon = $2
- Delivery fee = $10
- Total cost equation: \(C_E = 2b + 10\)

Where \(b\) is the number of balloons (30).

So, substituting 30 for \(b\):

\[
C_E = 2(30) + 10
\]
\[
C_E = 60 + 10 = 70
\]

**For Balloon Mania:**

- Price per balloon = $1.50
- Delivery fee = $20
- Total cost equation: \(C_M = 1.50b + 20\)

Again substituting 30 for \(b\):

\[
C_M = 1.50(30) + 20
\]
\[
C_M = 45 + 20 = 65
\]

Now we compare the costs:

- Cost with Balloon Express: $70
- Cost with Balloon Mania: $65

To find out which company is cheaper:

\[
\text{Savings} = C_E - C_M = 70 - 65 = 5
\]

So, Balloon Mania is the cheaper option, and the O'Donnells will save $5.

Thus, they should choose:

**Balloon Mania; $5**