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 Express; $25
Balloon Express; $25

Balloon Mania; $5
Balloon Mania; $5

Balloon Express; $5 
Balloon Express; $5

Balloon Mania; $25

GPT 3.5 · Answer

To solve this problem using a system of equations, we can set up the following equations:

Let x be the number of balloons ordered from Balloon Express.
Let y be the number of balloons ordered from Balloon Mania.

Equation 1: 2x + 10 = total cost for Balloon Express
Equation 2: 1.50y + 20 = total cost for Balloon Mania

Given that the O'Donnells plan to order 30 balloons, we know that x + y = 30.

To find out which company they should choose, we need to compare the total costs for both companies and see which one is cheaper.

Substituting x = 30 - y into equation 1, we have:
2(30 - y) + 10 = 60 - 2y + 10 = 70 - 2y

Comparing this with equation 2, we have:
70 - 2y = 1.50y + 20

Adding 2y to both sides of the equation:
70 = 3.50y + 20

Subtracting 20 from both sides of the equation:
50 = 3.50y

Dividing both sides by 3.50:
y = 14.29

Since we can't order fractions of balloons, we round y to the nearest whole number, which is 14.

Now, substituting y = 14 into equation 2:
1.50(14) + 20 = 21 + 20 = 41

Therefore, Balloon Mania charges $41 for 14 balloons.

Now, we can find x by subtracting y from the total number of balloons:
x = 30 - y = 30 - 14 = 16

Substituting x = 16 into equation 1:
2(16) + 10 = 32 + 10 = 42

Therefore, Balloon Express charges $42 for 16 balloons.

Comparing the costs, we can see that Balloon Mania charges less, $41 for 14 balloons, whereas Balloon Express charges $42 for 16 balloons.

Therefore, the O'Donnells should choose Balloon Mania, and they would save $1.