solve this real world problem using a system of equations. The o donnels 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 charged 1.50 per balloon and 20 for delivery. If the O'donnells plan to order 30 balloons which company should they school and how much will they save?

1 answer

Let's denote the total cost from Balloon Express as \(C_E\) and the total cost from Balloon Mania as \(C_M\).

For Balloon Express:

  • Cost per balloon = $2
  • Delivery fee = $10
  • Number of balloons = 30

The cost for balloons from Balloon Express can be calculated as: \[ C_E = (2 \times 30) + 10 \] \[ C_E = 60 + 10 = 70 \]

For Balloon Mania:

  • Cost per balloon = $1.50
  • Delivery fee = $20
  • Number of balloons = 30

The cost for balloons from Balloon Mania can be calculated as: \[ C_M = (1.50 \times 30) + 20 \] \[ C_M = 45 + 20 = 65 \]

Comparing Costs:

Now we can compare the total costs:

  • Cost from Balloon Express: \(C_E = 70\)
  • Cost from Balloon Mania: \(C_M = 65\)

Conclusion:

Balloon Mania is the cheaper option. To find out how much the O'Donnells will save by choosing Balloon Mania over Balloon Express: \[ \text{Savings} = C_E - C_M = 70 - 65 = 5 \]

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