Question Solve this real-world problem using a system of equations. The O’Donnells are having a birthday party for their son%2C and they plan to have a clown bring balloons to the party. Balloon Express charges %242 per balloon and %2410 for delivery. Balloon Mania charges %241.50 per balloon and %2420 for delivery. If the O’Donnells plan to order 30 balloons%2C which company should they choose%2C and how much will they save%3F(1 point) Responses Balloon Mania%3B %2425 Balloon Mania%3B %2425 Balloon Express%3B %245 Balloon Express%3B %245 Balloon Mania%3B %245 Balloon Mania%3B %245 Balloon Express%3B %2425
To solve this problem, we can set up a system of equations.
Let x be the number of balloons and y be the delivery cost.
For Balloon Express:
Cost of balloons: 2x
Delivery cost: 10
Total cost: 2x + 10
For Balloon Mania:
Cost of balloons: 1.5x
Delivery cost: 20
Total cost: 1.5x + 20
We are given that the O'Donnells plan to order 30 balloons.
Substituting x = 30 into the equations above:
For Balloon Express: 2(30) + 10 = 60 + 10 = 70
For Balloon Mania: 1.5(30) + 20 = 45 + 20 = 65
Therefore, the O'Donnells should choose Balloon Mania as it will cost $65 compared to $70 with Balloon Express.
They will save $70 - $65 = $5.
Therefore, the correct answer is:
Balloon Mania; $5.
To solve this problem, we need to compare the total cost of ordering 30 balloons from both companies.
Let's assume the number of balloons from Balloon Express is B1 and the number of balloons from Balloon Mania is B2.
According to the given information:
Balloon Express charges $2 per balloon and $10 for delivery.
So, the cost of ordering balloons from Balloon Express can be represented as:
Cost of balloons from Balloon Express (C1) = 2*B1 + 10
Balloon Mania charges $1.50 per balloon and $20 for delivery.
So, the cost of ordering balloons from Balloon Mania can be represented as:
Cost of balloons from Balloon Mania (C2) = 1.5*B2 + 20
We know the O'Donnells plan to order 30 balloons. So, we have the following constraint:
B1 + B2 = 30
To find the company that the O'Donnells should choose and how much they will save, we need to solve this system of equations:
Equation 1: C1 = 2*B1 + 10
Equation 2: C2 = 1.5*B2 + 20
Equation 3: B1 + B2 = 30
Now, let's solve the system of equations:
1) Multiply Equation 3 by 2: 2*(B1 + B2) = 2*(30)
Simplifying, we get: 2*B1 + 2*B2 = 60
2) Subtract Equation 1 from Equation 2: C2 - C1 = (1.5*B2 + 20) - (2*B1 + 10)
Simplifying, we get: 0.5*B2 - 2*B1 + 10 = 0
3) Substitute the value of 2*B1 from Equation 1 into Equation 2:
0.5*B2 - (2*B1 + 10) + 10 = 0
Simplifying, we get: 0.5*B2 - 2*B1 = 0
Now, we have the following system of equations:
2*B1 + 2*B2 = 60
0.5*B2 - 2*B1 = 0
Solving this system, we find B1 = 15 and B2 = 15.
Now, let's calculate the cost for both companies:
For Balloon Express:
C1 = 2*B1 + 10 = 2*15 + 10 = 40
For Balloon Mania:
C2 = 1.5*B2 + 20 = 1.5*15 + 20 = 42.5
Comparing the costs, we see that Balloon Express charges $40 and Balloon Mania charges $42.5.
Therefore, the O'Donnells should choose Balloon Express and they will save $42.5 - $40 = $2.5.
To solve this real-world problem using a system of equations, we need to compare the costs from both companies for ordering 30 balloons.
Let's set up the equations:
For Balloon Express:
Cost per balloon: $2
Delivery cost: $10
Total cost for 30 balloons: 2(30) + 10 = $60 + $10 = $70
For Balloon Mania:
Cost per balloon: $1.50
Delivery cost: $20
Total cost for 30 balloons: 1.50(30) + 20 = $45 + $20 = $65
Comparing the total costs, we see that Balloon Mania charges $65, while Balloon Express charges $70. Therefore, the O'Donnells should choose Balloon Mania as it would be cheaper.
To calculate the amount they would save, we subtract the cost from Balloon Mania from the cost from Balloon Express:
$70 - $65 = $5
So, the O'Donnells would save $5 by choosing Balloon Mania over Balloon Express.