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)ResponsesBalloon Express; $5 Balloon Express; $5 Balloon Mania; $5Balloon Mania; $5Balloon Mania; $25 Balloon Mania; $25 Balloon Express; $25

1 answer

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

The cost of Balloon Express is given by the equation 2x + 10.
The cost of Balloon Mania is given by the equation 1.5y + 20.

We are given that the total number of balloons ordered is 30, so x + y = 30.

To determine which company the O'Donnells should choose, we need to compare the costs of each option.

For Balloon Express: Cost = 2x + 10
For Balloon Mania: Cost = 1.5y + 20

We can substitute the value of x from the equation x + y = 30 into the cost equation for Balloon Express:

Cost = 2(30 - y) + 10
Cost = 60 - 2y + 10
Cost = 70 - 2y

To determine which option is cheaper, we need to compare the cost equations of Balloon Express and Balloon Mania:

70 - 2y < 1.5y + 20

Simplifying this inequality:

70 < 3.5y + 20
50 < 3.5y

Dividing both sides by 3.5:

14.29 < y

Since the number of balloons cannot be a fraction, the O'Donnells must choose Balloon Mania and order 15 balloons.

To determine the cost savings, we can substitute the value of y = 15 into the cost equation for Balloon Mania:

Cost = 1.5(15) + 20
Cost = 22.5 + 20
Cost = 42.5

Therefore, the O'Donnells should choose Balloon Mania and save $42.5 compared to Balloon Express.