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?
A. Balloon Express; $5
B. Balloon Mania; $25
C. Balloon Express; 25
D. $25 Balloon Mania; $5
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.
To solve this problem, we can set up a system of equations and solve for the total cost of each company.
Let's denote the number of balloons as x.
For Balloon Express, the cost can be represented as: Cost_Express = 2x + 10
For Balloon Mania, the cost can be represented as: Cost_Mania = 1.50x + 20
We know that the O'Donnells plan to order 30 balloons, so x = 30.
Now we can substitute x = 30 into the equations to find the costs for each company:
Cost_Express = 2(30) + 10 = 60 + 10 = 70
Cost_Mania = 1.50(30) + 20 = 45 + 20 = 65
Comparing the costs, we can see that the O'Donnells should choose Balloon Mania, as it would cost them $65. Choosing Balloon Express would cost them $70.
To find the amount they will save, we subtract the cost of Balloon Mania from the cost of Balloon Express:
Savings = Cost_Express - Cost_Mania = 70 - 65 = 5
Therefore, the correct answer is:
C. Balloon Express; $5
To solve this real-world problem using a system of equations, we need to set up the equations representing the costs for each company and find the solution that minimizes the total cost. Let's define some variables:
Let x represent the number of balloons from Balloon Express.
Let y represent the number of balloons from Balloon Mania.
Based on the given information, we can form the following two 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 a total of 30 balloons, so we have the additional constraint:
Equation 3: x + y = 30.
We can now solve this system of equations to find the values of x and y. Let's rewrite Equation 3 as x = 30 - y and substitute it into Equations 1 and 2:
Equation 1: 2(30 - y) + 10 = total cost for Balloon Express.
Equation 2: 1.5y + 20 = total cost for Balloon Mania.
Simplifying Equation 1:
60 - 2y + 10 = total cost for Balloon Express.
70 - 2y = total cost for Balloon Express.
Now we can compare the costs of the two companies:
Balloon Express: 70 - 2y.
Balloon Mania: 1.5y + 20.
Since the O'Donnells plan to order 30 balloons, we substitute y = 30 into the equations:
Balloon Express: 70 - 2(30) = 70 - 60 = $10.
Balloon Mania: 1.5(30) + 20 = 45 + 20 = $65.
Based on the calculations, the total cost for Balloon Express is $10 and for Balloon Mania is $65. The O'Donnells should choose Balloon Express. To find out how much they will save, we subtract the cost of Balloon Express from Balloon Mania: $65 - $10 = $55.
Therefore, the correct answer is B. Balloon Mania; $55.