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?

Responses

Balloon Express; $25

Balloon Mania; $25 

Balloon Express; $5

Balloon Mania; $5

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this problem, we can set up a system of equations. Let's represent the number of balloons ordered as x.

For Balloon Express, the cost can be calculated as:
Cost_balloon_express = 2x + 10 (where 2x represents the cost of the balloons and 10 represents the delivery fee)

For Balloon Mania, the cost can be calculated as:
Cost_balloon_mania = 1.50x + 20 (where 1.50x represents the cost of the balloons and 20 represents the delivery fee)

Since the O'Donnells plan to order 30 balloons, we can plug in x=30 into the equations above to find the total cost.

Cost_balloon_express = 2(30) + 10 = 60 + 10 = 70
Cost_balloon_mania = 1.50(30) + 20 = 45 + 20 = 65

Therefore, the O'Donnells should choose Balloon Mania because they will save $5 by choosing them instead of Balloon Express.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To solve this problem using a system of equations, let's represent the number of balloons ordered as "x" and the total cost as "y".

For Balloon Express:
Cost per balloon: $2
Delivery fee: $10
Total cost: 2x + 10

For Balloon Mania:
Cost per balloon: $1.50
Delivery fee: $20
Total cost: 1.5x + 20

Since the O'Donnells plan to order 30 balloons, we can substitute x = 30 into the equations to find the total cost for each company.

For Balloon Express:
Total cost = 2x + 10
Substituting x = 30:
Total cost = 2(30) + 10
Total cost = 60 + 10
Total cost = $70

For Balloon Mania:
Total cost = 1.5x + 20
Substituting x = 30:
Total cost = 1.5(30) + 20
Total cost = 45 + 20
Total cost = $65

Comparing the total costs, the O'Donnells should choose Balloon Mania as it will cost them $65. Choosing Balloon Express would cost them $70. Therefore, they will save $5 by choosing Balloon Mania.

So the answer is Balloon Mania; $5.

Answer 3

[AI-generated answer — Explain Bot]

To solve this problem using a system of equations, we need to set up two equations that represent the total cost for each company.

Let's define the variables:
Let B = number of balloons
Let C = cost of balloons
Let D = delivery charge

For Balloon Express, the total cost can be represented as:
C(B) + D = 2B + 10

For Balloon Mania, the total cost can be represented as:
C(B) + D = 1.5B + 20

Since the O'Donnells plan to order 30 balloons, we can substitute B = 30 into the equations.

For Balloon Express:
2(30) + 10 = 60 + 10 = 70

For Balloon Mania:
1.5(30) + 20 = 45 + 20 = 65

Therefore, Balloon Express will cost $70 while Balloon Mania will cost $65.

To find how much they will save, we subtract the cost of Balloon Mania from Balloon Express.

70 - 65 = $5

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