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)
Responses
Balloon Mania; $25
Balloon Mania; $25
Balloon Express; $25
Balloon Express; $25
Balloon Mania; $5
Balloon Mania; $5
Balloon Express; $5
To solve this problem using a system of equations, let's represent the number of balloons as "x".
For Balloon Express, the total cost would be $2x + $10 for delivery.
For Balloon Mania, the total cost would be $1.50x + $20 for delivery.
Since the O'Donnells plan to order 30 balloons, we can substitute "x" with 30 in the equations.
For Balloon Express, the total cost would be $2(30) + $10 = $60 + $10 = $70.
For Balloon Mania, the total cost would be $1.50(30) + $20 = $45 + $20 = $65.
Therefore, the O'Donnells should choose Balloon Mania as it is the cheaper option. They will save $70 - $65 = $5.
So the correct answer is: Balloon Mania; $5.
To solve this problem using a system of equations, let's introduce variables to represent the unknown quantities.
Let:
x = number of balloons ordered from Balloon Express
y = number of balloons ordered from Balloon Mania
According to the problem, the O'Donnells plan to order 30 balloons in total. This gives us the first equation:
x + y = 30
Next, we need to find the total cost for each company.
For Balloon Express, each balloon costs $2, and there is a $10 delivery charge, so the total cost for x balloons from Balloon Express is:
2x + 10
For Balloon Mania, each balloon costs $1.50, and there is a $20 delivery charge, so the total cost for y balloons from Balloon Mania is:
1.50y + 20
The O'Donnells want to determine which company to choose based on cost. Therefore, the second equation is:
2x + 10 = 1.50y + 20
Now we have a system of equations:
x + y = 30
2x + 10 = 1.50y + 20
To solve this system, we can use the substitution or elimination method. Let's use the substitution method.
Rearrange the first equation:
x = 30 - y
Substitute this value of x into the second equation:
2(30 - y) + 10 = 1.50y + 20
Simplify the equation:
60 - 2y + 10 = 1.50y + 20
70 - 2y = 1.50y + 20
Combine like terms:
-2y - 1.50y = 20 - 70
-3.50y = -50
y = -50 / -3.50
y = 14.29
Since y represents the number of balloons, it must be a whole number. Therefore, we can round it to the nearest whole number: y = 14.
Substitute the value of y back into the first equation to find x:
x + 14 = 30
x = 30 - 14
x = 16
So, the O'Donnells should choose Balloon Express and order 16 balloons from them. The cost of Balloon Express would be:
2(16) + 10 = $42
The cost of Balloon Mania for 14 balloons would be:
1.50(14) + 20 = $41
Therefore, the O'Donnells would save $1 by choosing Balloon Express. The correct answer is Balloon Express; $1
To solve this problem using a system of equations, let's set up two equations to represent the cost of balloons from each company.
Let's represent the number of balloons from Balloon Express as x and the number of balloons from Balloon Mania as y.
The cost equation for Balloon Express would be:
Cost_Express = 2x + 10 (since they charge $2 per balloon and $10 for delivery)
The cost equation for Balloon Mania would be:
Cost_Mania = 1.5y + 20 (since they charge $1.50 per balloon and $20 for delivery)
We know that the O'Donnells plan to order 30 balloons, so the total number of balloons must be 30, which gives us the equation:
x + y = 30
Now we have a system of equations:
Cost_Express = 2x + 10
Cost_Mania = 1.5y + 20
x + y = 30
To solve the system, we can substitute the value of x from the third equation into the first and second equations.
x = 30 - y
Substituting this into the first equation:
Cost_Express = 2(30 - y) + 10
Cost_Express = 60 - 2y + 10
Cost_Express = 70 - 2y
Substituting this into the second equation:
Cost_Mania = 1.5y + 20
Now we have two equations in terms of only one variable, y. To find the cost for each company, we need to substitute different values of y into the equations and compare the results.
Let's start with y = 10:
Cost_Express = 70 - 2(10) = 50
Cost_Mania = 1.5(10) + 20 = 35
So, if the O'Donnells choose Balloon Mania with 10 balloons, they would pay $35.
Let's try y = 20:
Cost_Express = 70 - 2(20) = 30
Cost_Mania = 1.5(20) + 20 = 50
So, if the O'Donnells choose Balloon Express with 20 balloons, they would pay $30.
Comparing the two options, we see that Balloon Express is the cheaper option when ordering 20 balloons. Therefore, the O'Donells should choose Balloon Express and save $5 in total. So the correct answer is "Balloon Express; $5".