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;
D. $25 Balloon Mania; $5
To solve this problem, we need to create a system of equations. Let's assume that x is the cost per balloon from Balloon Express and y is the cost per balloon from Balloon Mania.
According to the problem:
Balloon Express charges $2 per balloon and $10 for delivery.
So the total cost from Balloon Express is 2x + 10.
Balloon Mania charges $1.50 per balloon and $20 for delivery.
So the total cost from Balloon Mania is 1.5x + 20.
Since they plan to order 30 balloons, we can equate the total cost from both companies:
2x + 10 = 1.5x + 20.
Now, let's solve this equation:
2x - 1.5x = 20 - 10,
0.5x = 10,
x = 10 / 0.5,
x = 20.
Substitute x = 20 into either equation to find the total cost from each company:
Total cost from Balloon Express = 2(20) + 10 = 40 + 10 = 50.
Total cost from Balloon Mania = 1.5(20) + 20 = 30 + 20 = 50.
Since both companies have the same total cost, they should choose either company. Therefore, the correct answer is option C: Balloon Express. However, the problem does not provide information on how much they will save, so it's not possible to determine the amount of savings. Thus, the answer choices provided are not correct.
To solve this problem, let's set up a system of equations.
Let's assume the number of balloons ordered is "x".
For Balloon Express:
The total cost would be 2x + 10.
For Balloon Mania:
The total cost would be 1.5x + 20.
Since the O'Donnells plan to order 30 balloons (x = 30), let's calculate the costs for each company.
For Balloon Express:
Total cost = 2(30) + 10 = 60 + 10 = 70.
For Balloon Mania:
Total cost = 1.5(30) + 20 = 45 + 20 = 65.
Therefore, the O'Donnells should choose Balloon Mania because it would cost them $65 compared to Balloon Express, which would cost them $70.
The amount they would save by choosing Balloon Mania over Balloon Express is $70 - $65 = $5.
So, the correct answer is:
Option D: Balloon Mania; $5
To solve this real-world problem using a system of equations, we can set up two equations representing the total cost for each company.
Let's use the variables:
- x for the number of balloons from Balloon Express
- y for the number of balloons from Balloon Mania
From the given information, we can create the following equations:
Equation 1:
The total cost for Balloon Express = $2 per balloon(x) + $10 delivery
Equation 2:
The total cost for Balloon Mania = $1.50 per balloon(y) + $20 delivery
Since the O’Donnells plan to order a total of 30 balloons, we know that x + y = 30.
To find out which company they should choose, we need to compare the total costs.
First, let's substitute x = 30 - y into Equation 1:
Total cost for Balloon Express = $2 per balloon(30 - y) + $10 delivery
= $60 - $2y + $10
= $70 - $2y
Now, let's substitute x = 30 - y into Equation 2:
Total cost for Balloon Mania = $1.50 per balloon(y) + $20 delivery
= $1.50y + $20
So, we have the two equations:
Total cost for Balloon Express = $70 - $2y ---(Equation 3)
Total cost for Balloon Mania = $1.50y + $20 ---(Equation 4)
To determine which company the O'Donnells should choose, we need to find the values of y that make the total cost for Balloon Express and Balloon Mania equal.
Let's set up an equation with Equation 3 and Equation 4:
$70 - $2y = $1.50y + $20
Simplifying the equation, we get:
$70 - $20 = $1.50y + $2y
$50 = $3.50y
Dividing both sides by $3.50, we find:
y = $50 / $3.50
y = 14.29
Since we can't have a fraction of a balloon, let's round down to the nearest whole number:
y ≈ 14
Now that we have the value of y, we can substitute it back into Equation 3 to find the total cost for Balloon Express:
Total cost for Balloon Express = $70 - $2y
= $70 - $2(14)
= $70 - $28
= $42
Finally, we can compare the total costs for Balloon Express and Balloon Mania:
Total cost for Balloon Express = $42
Total cost for Balloon Mania = $1.50y + $20
= $1.50(14) + $20
= $21 + $20
= $41
Therefore, the O'Donnells should choose Balloon Mania, and they will save $1 compared to Balloon Express. However, none of the given answer choices match the correct solution.