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;
B. $5 Balloon Express;
C. $5 Balloon Mania; $25 Balloon Mania; $25 Balloon Express;
D. $25 Balloon Express; $25 Balloon Mania; $5
Let's solve this problem using a system of equations.
Let
x = number of balloons
y = cost for delivery
Based on the given information, we can set up the following equations:
For Balloon Express:
Cost = 2x + 10
For Balloon Mania:
Cost = 1.50x + 20
We know that the O'Donnells plan to order 30 balloons, so we can substitute x = 30 into both equations:
For Balloon Express:
Cost = 2(30) + 10
Cost = 60 + 10
Cost = 70
For Balloon Mania:
Cost = 1.50(30) + 20
Cost = 45 + 20
Cost = 65
Therefore, the O'Donnells should choose Balloon Mania as they will save $5 compared to Balloon Express. The correct answer is option C: $5 Balloon Mania; $25 Balloon Express.
To solve this real-world problem using a system of equations, we need to set up equations for each company, representing the total cost based on the number of balloons ordered.
Let's assume:
x = number of balloons ordered
y = total cost for Balloon Express
z = total cost for Balloon Mania
For Balloon Express:
Cost per balloon = $2
Delivery charge = $10
Total cost for Balloon Express = 2x + 10y
For Balloon Mania:
Cost per balloon = $1.50
Delivery charge = $20
Total cost for Balloon Mania = 1.5x + 20z
Given that the O’Donnells plan to order 30 balloons, we can substitute x = 30 into both equations:
For Balloon Express:
y = Total cost for Balloon Express
y = 2(30) + 10
y = 60 + 10
y = 70
For Balloon Mania:
z = Total cost for Balloon Mania
z = 1.5(30) + 20
z = 45 + 20
z = 65
So, the total cost for Balloon Express with 30 balloons is $70, and the total cost for Balloon Mania with 30 balloons is $65.
To determine which company the O’Donnells should choose and how much they will save, we compare the costs:
Total cost for Balloon Express = $70
Total cost for Balloon Mania = $65
Since the total cost for Balloon Mania with 30 balloons is $65 and is less than the total cost for Balloon Express with 30 balloons at $70, the O’Donnells should choose Balloon Mania.
To find out how much they will save, subtract the total cost with Balloon Mania from the total cost with Balloon Express:
Savings = Total cost for Balloon Express - Total cost for Balloon Mania
Savings = $70 - $65
Savings = $5
Therefore, the O’Donnells should choose Balloon Mania and they will save $5.
The correct answer is B. $5 Balloon Express.
To solve this real-world problem using a system of equations, we can set up two equations based on the information given.
Let's assume x represents the number of balloons ordered from Balloon Express and y represents the number of balloons ordered from Balloon Mania.
Equation 1: Balloon Express cost
2x + 10
Equation 2: Balloon Mania cost
1.5y + 20
The problem states that the O'Donnells plan to order 30 balloons, so we can set up a third equation based on this information.
Equation 3: Total number of balloons
x + y = 30
To find which company the O'Donnells should choose, we need to compare the costs. Let's substitute the value of y in terms of x from Equation 3 into Equation 2.
1.5y + 20 = 1.5(30 - x) + 20
1.5y + 20 = 45 - 1.5x + 20
1.5y = 45 - 1.5x
Now we can set the two cost equations equal to each other and solve for x.
2x + 10 = 1.5y + 20
Substitute y = 30 - x.
2x + 10 = 1.5(30 - x) + 20
2x + 10 = 45 - 1.5x + 20
2.5x = 55
x = 22
Now substitute the value of x into Equation 3 to find y.
22 + y = 30
y = 30 - 22
y = 8
So, the O'Donnells should order 22 balloons from Balloon Express and 8 balloons from Balloon Mania.
To find out how much they will save, we can calculate the costs for both companies.
Balloon Express cost: 2x + 10
= 2(22) + 10
= 44 + 10
= $54
Balloon Mania cost: 1.5y + 20
= 1.5(8) + 20
= 12 + 20
= $32
The O'Donnells will save the difference between the two costs: $54 - $32 = $22.
Therefore, the correct answer is D. $25 Balloon Express; $25 Balloon Mania; $5. They will save $22, not $5.