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)

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 Mania; $25 
Balloon Mania; $25

Balloon Express; $25
Balloon Express; $25

Balloon Express; $5

GPT 3.5 · Answer

To solve this problem using a system of equations, let's assign variables to the unknowns.

Let's say B represents the number of balloons ordered from Balloon Express and M represents the number of balloons ordered from Balloon Mania.

From the given information, we can form two equations:

1) Balloon Express charges $2 per balloon and $10 for delivery, so the total cost for ordering B balloons is 2B + 10.

2) Balloon Mania charges $1.50 per balloon and $20 for delivery, so the total cost for ordering M balloons is 1.50M + 20.

We are given that the O'Donnells plan to order 30 balloons, so B + M = 30.

Now we can set up the system of equations:

2B + 10 = 1.50M + 20 (equation 1)
B + M = 30 (equation 2)

To solve this system, we can use substitution or elimination. Let's use substitution:

We can isolate B in equation 2 and substitute it into equation 1:

B = 30 - M (equation 3)

Now substitute equation 3 into equation 1:

2(30 - M) + 10 = 1.50M + 20

Distribute and combine like terms:

60 - 2M + 10 = 1.50M + 20

70 - 2M = 1.50M + 20

Simplify:

-2M - 1.50M = 20 - 70

-3.50M = -50

Divide by -3.50 to solve for M:

M = (-50) / (-3.50)

M = 14.29

Since we cannot have a fraction of a balloon, we can round M up to the nearest whole number, which is 15.

Substitute M = 15 back into equation 3 to solve for B:

B = 30 - 15

B = 15

Therefore, the O'Donnells should choose Balloon Mania to order 15 balloons, and they will save $25 compared to ordering from Balloon Express.

So, the correct answer is:
Balloon Mania; $25