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?

Question

A. Balloon Express; $5
B. Balloon Mania; $25
C. Balloon Express; 25
D. $25 Balloon Mania; $5

Answer 1

Let's let x represent the number of balloons ordered from Balloon Express and y represent the number of balloons ordered from Balloon Mania.

According to the given information, we can set up the following system of equations:

1) 2x + 10 = 30 (cost for Balloon Express)
2) 1.50y + 20 = 30 (cost for Balloon Mania)

Simplifying equation 1, we get:
2x + 10 = 30
Subtracting 10 from both sides, we get:
2x = 20
Dividing both sides by 2, we get:
x = 10

Simplifying equation 2, we get:
1.50y + 20 = 30
Subtracting 20 from both sides, we get:
1.50y = 10
Dividing both sides by 1.50, we get:
y = 6.67

Since we can't have a fractional number of balloons, we can round up to the nearest whole number, so y = 7.

Now we can calculate the total cost for each company:

For Balloon Express:
Total cost = (cost per balloon * number of balloons) + delivery cost
Total cost = (2 * 10) + 10
Total cost = 20 + 10
Total cost = 30

For Balloon Mania:
Total cost = (cost per balloon * number of balloons) + delivery cost
Total cost = (1.50 * 7) + 20
Total cost = 10.50 + 20
Total cost = 30.50

So the O'Donnells should choose Balloon Express, and they will save $0.50 (not $5 or $25).

Thus, the correct answer is D. $25 Balloon Mania; $5.