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
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.
To solve this problem using a system of equations, we need to set up equations for the total cost of each company's services.
Let's say x represents the number of balloons and y represents the cost in dollars.
For Balloon Express, the cost can be represented as:
y = 2x + 10
For Balloon Mania, the cost can be represented as:
y = 1.50x + 20
Since the O'Donnells plan to order 30 balloons, we can substitute x = 30 into both equations:
For Balloon Express:
y = 2(30) + 10
y = 60 + 10
y = 70
For Balloon Mania:
y = 1.50(30) + 20
y = 45 + 20
y = 65
Comparing the total costs, we can see that Balloon Mania charges $65, while Balloon Express charges $70. Therefore, the O'Donnells should choose Balloon Mania.
To determine the amount they will save, we subtract the cost of Balloon Mania from the cost of Balloon Express:
$70 - $65 = $5
So they will save $5 by choosing Balloon Mania.
To solve this real-world problem using a system of equations, we need to set up equations to represent the costs of the two balloon companies. Let's denote the number of balloons as 'b' and the cost of delivery as 'd'.
For Balloon Express:
Cost of balloons = $2 per balloon
Delivery cost = $10
Total cost = 2b + 10
Equation 1: Total cost for Balloon Express = 2b + 10
For Balloon Mania:
Cost of balloons = $1.50 per balloon
Delivery cost = $20
Total cost = 1.50b + 20
Equation 2: Total cost for Balloon Mania = 1.50b + 20
Since the O'Donnells plan to order 30 balloons, we can substitute b = 30 into the equations.
For Balloon Express:
Total cost = 2(30) + 10
Total cost = 60 + 10
Total cost = $70
For Balloon Mania:
Total cost = 1.50(30) + 20
Total cost = 45 + 20
Total cost = $65
Therefore, the O'Donnells should choose Balloon Mania because the total cost is $65. They would save $5 compared to choosing Balloon Express.