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; $25 
Balloon Mania; $25 

Balloon Express; $25
Balloon Express; $25

Balloon Express; $5
Balloon Express; $5

Balloon Mania; $5
Balloon Mania; $5

2 answers

To determine which company the O’Donnells should choose for the balloons, we can set up two equations representing the total cost for each company based on the cost of balloons plus the delivery fee.

Let:

  • \( x \) be the number of balloons (which is 30).
  1. Balloon Express Cost:

    • Cost per balloon: $2
    • Delivery fee: $10
    • Total cost \( C_E \) for Balloon Express: \[ C_E = 2x + 10 \]
  2. Balloon Mania Cost:

    • Cost per balloon: $1.50
    • Delivery fee: $20
    • Total cost \( C_M \) for Balloon Mania: \[ C_M = 1.5x + 20 \]

Now, substituting \( x = 30 \) into both equations:

For Balloon Express: \[ C_E = 2(30) + 10 = 60 + 10 = 70 \]

For Balloon Mania: \[ C_M = 1.5(30) + 20 = 45 + 20 = 65 \]

Now, we can compare the total costs:

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

Now, we calculate the savings:

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

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

The correct response is: Balloon Mania; $5

The Spanish Club at Santa Fe Middle School wants to sell mini quiches to raise money for a field trip. The culinary department at their school will make the quiches for $30 plus $0.50 per quiche for the ingredients. The Spanish Club wants to sell each quiche for $2. How many quiches will they need to sell in order to break even?(1 point)
Responses

12 quiches
12 quiches

20 quiches
20 quiches

75 quiches
75 quiches

45 quiches