olve 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; $25 Balloon Mania; $25 Balloon Mania; $5 Balloon Mania; $5 Balloon Express; $5 Balloon Express; $5 Balloon Express; $25 Balloon Express; $25
Let's denote the number of balloons ordered as "x".
For Balloon Express, the cost equation is:
Cost of balloons = 2x
Delivery cost = 10
Total cost = 2x + 10
For Balloon Mania, the cost equation is:
Cost of balloons = 1.50x
Delivery cost = 20
Total cost = 1.50x + 20
Since the O'Donnells plan to order 30 balloons, we can substitute x = 30 into the cost equations:
For Balloon Express: Total cost = 2(30) + 10 = 60 + 10 = $70
For Balloon Mania: Total cost = 1.50(30) + 20 = 45 + 20 = $65
Therefore, the O'Donnells should choose Balloon Mania and they will save $70 - $65 = $5.
Let x be the number of balloons from Balloon Express and y be the number of balloons from Balloon Mania.
According to the given information, we have the following equations:
Equation 1: 2x + 10 = total cost for Balloon Express
Equation 2: 1.5y + 20 = total cost for Balloon Mania
We know that the O'Donnells plan to order 30 balloons, so x + y = 30.
To find the solution, we can solve the system of equations.
Substituting x = 30 - y into Equation 1, we get:
2(30 - y) + 10 = total cost for Balloon Express
60 - 2y + 10 = total cost for Balloon Express
70 - 2y = total cost for Balloon Express
Substituting x = 30 - y into Equation 2, we get:
1.5y + 20 = total cost for Balloon Mania
To compare the costs, we need to evaluate both expressions for the total cost:
Balloon Express: 70 - 2y
Balloon Mania: 1.5y + 20
Since the O'Donnells plan to order 30 balloons, we can evaluate the cost for each company:
Balloon Express: 70 - 2(30) = 70 - 60 = $10
Balloon Mania: 1.5(30) + 20 = 45 + 20 = $65
From the calculations, we can see that the O'Donnells should choose Balloon Express because it offers a lower cost. The cost difference is $65 - $10 = $55.
Therefore, the correct answer is: Balloon Express; $55
To solve this real-world problem using a system of equations, we need to set up equations to represent the cost of the balloons and delivery fees for both companies. Let's define the variables:
Let 'x' be the cost per balloon from Balloon Express.
Let 'y' be the cost per balloon from Balloon Mania.
From the given information, we have two equations:
Equation 1: 2x + 10 = total cost for Balloon Express
Equation 2: 1.5y + 20 = total cost for Balloon Mania
We also know that the O'Donnells plan to order 30 balloons. So we can add another equation:
Equation 3: x + y = 30 (since the total number of balloons is 30)
Now, we have a system of three equations:
2x + 10 = total cost for Balloon Express
1.5y + 20 = total cost for Balloon Mania
x + y = 30
We can solve this system of equations to find the values of 'x' and 'y'. Let's solve the system:
From Equation 3, we can rewrite it as: x = 30 - y
Substituting this value of x into Equation 1, we get:
2(30 - y) + 10 = total cost for Balloon Express
60 - 2y + 10 = total cost for Balloon Express
70 - 2y = total cost for Balloon Express
Now, we can compare the total cost for both companies:
Balloon Express: 70 - 2y (total cost)
Balloon Mania: 1.5y + 20 (total cost)
To determine the cheaper option, we compare the total costs for 30 balloons from each company:
70 - 2y < 1.5y + 20
Simplifying the inequality, we have:
70 < 1.5y + 2y + 20
70 < 3.5y + 20
50 < 3.5y
14.29 < y
Since the cost per balloon from Balloon Mania (y) must be greater than 14.29, the only option that satisfies this condition is y = 15.
Substituting y = 15 into Equation 3, we get:
x + 15 = 30
x = 30 - 15
x = 15
Therefore, the cost per balloon from Balloon Express (x) is 15.
Comparing the total costs:
Balloon Express: 70 - 2y = 70 - 2(15) = 40
Balloon Mania: 1.5y + 20 = 1.5(15) + 20 = 22.5 + 20 = 42.5
Balloon Express charges $40 in total, while Balloon Mania charges $42.5 in total.
The O'Donnells should choose Balloon Express because they will save $2.5 compared to Balloon Mania ($42.5 - $40 = $2.5).