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? (1 point)
Balloon Express: $25
Balloon Mania: $5
Balloon Mania: $25
Balloon Express, $5
Let's represent the cost of ordering balloons from Balloon Express as E and the cost of ordering balloons from Balloon Mania as M.
From the information given, we know that:
E = 2 * number of balloons + 10
M = 1.50 * number of balloons + 20
We also know that the O'Donnells plan to order 30 balloons:
number of balloons = 30
Using these equations, we can find the cost for each company:
E = 2 * 30 + 10
E = 60 + 10
E = 70
M = 1.50 * 30 + 20
M = 45 + 20
M = 65
Therefore, the O'Donnells should choose Balloon Mania because they will save $5 compared to Balloon Express.
To solve this real-world problem using a system of equations, we can set up two equations representing the costs of the two companies. Let's assume x represents the number of balloons ordered and y represents the total cost.
For Balloon Express:
Cost per balloon = $2
Delivery charge = $10
The total cost for Balloon Express can be represented as:
y = 2x + 10
For Balloon Mania:
Cost per balloon = $1.50
Delivery charge = $20
The total cost for Balloon Mania can be represented as:
y = 1.5x + 20
Since the O'Donnells plan to order 30 balloons, we can substitute x = 30 into both equations to find the cost for each company.
For Balloon Express:
y = 2(30) + 10
y = 60 + 10
y = 70
For Balloon Mania:
y = 1.5(30) + 20
y = 45 + 20
y = 65
Therefore, the O'Donnells should choose Balloon Mania as they would save $5 compared to Balloon Express.
To solve this problem using a system of equations, let's define some variables:
Let x be the number of balloons from Balloon Express
Let y be the number of balloons from Balloon Mania
The cost for Balloon Express can be represented by the equation:
Cost of Balloon Express (CBE) = 2x + 10
The cost for Balloon Mania can be represented by the equation:
Cost of Balloon Mania (CBM) = 1.5y + 20
We know that the O'Donnells plan to order a total of 30 balloons, so we have the equation:
x + y = 30
To find out which company they should choose, we need to solve this system of equations.
Substitute x + y = 30 in the equation CBE:
CBE = 2x + 10
2x + 10 = CBE
Substitute x + y = 30 in the equation CBM:
CBM = 1.5y + 20
1.5y + 20 = CBM
Since we know from the problem that CBE = $25, we can substitute in this value:
2x + 10 = $25
Simplify the equation:
2x = 25 - 10
2x = 15
x = 15/2
x = 7.5
Now, substitute x = 7.5 into the equation x + y = 30:
7.5 + y = 30
Solve for y:
y = 30 - 7.5
y = 22.5
Now we have the values for x and y.
The O'Donnells choose Balloon Express if they buy 7.5 balloons from them and 22.5 balloons from Balloon Mania.
Now, let's compare the costs:
Cost of Balloon Express (CBE) = 2x + 10 = 2(7.5) + 10 = 15 + 10 = $25
Cost of Balloon Mania (CBM) = 1.5y + 20 = 1.5(22.5) + 20 = 33.75 + 20 = $53.75
Based on the calculations, the O'Donnells should choose Balloon Express, as it will cost them $25.
They will save:
Savings = Cost of Balloon Mania - Cost of Balloon Express
Savings = $53.75 - $25
Savings = $28.75
Therefore, the O'Donnells will save $28.75 by choosing Balloon Express.