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 Express; $25 Balloon Express; $25 Balloon Mania; $25 Balloon Mania; $25 Balloon Express; $5 Balloon Express; $5 Balloon Mania; $5 Balloon Mania; $5
To solve this problem using a system of equations, we can set up two equations representing the total cost for each company.
Let's assume the number of balloons ordered is x.
For Balloon Express, the total cost would be: 2x + 10 (2 dollars per balloon plus a 10-dollar delivery fee)
For Balloon Mania, the total cost would be: 1.5x + 20 (1.50 dollars per balloon plus a 20-dollar delivery fee)
Since the O'Donnells plan to order 30 balloons, we can substitute x = 30 into the equations:
For Balloon Express: Cost = 2(30) + 10 = 60 + 10 = 70 dollars
For Balloon Mania: Cost = 1.5(30) + 20 = 45 + 20 = 65 dollars
Therefore, they should choose Balloon Mania, and they will save:
70 - 65 = 5 dollars
To solve this problem using a system of equations, let's assume that x represents the number of balloons ordered from Balloon Express and y represents the number of balloons ordered from Balloon Mania.
From the given information, we can create the following equations:
For Balloon Express:
Cost of balloons = 2x
Cost of delivery = 10
Total cost for Balloon Express = 2x + 10
For Balloon Mania:
Cost of balloons = 1.5y
Cost of delivery = 20
Total cost for Balloon Mania = 1.5y + 20
Since the O’Donnells plan to order 30 balloons, we know that x + y = 30.
To find out which company they should choose, we need to compare the total costs of both companies.
For Balloon Express: total cost = 2x + 10
For Balloon Mania: total cost = 1.5y + 20
Now, let's substitute x = 30 - y into the equation for Balloon Express:
Total cost for Balloon Express = 2(30 - y) + 10
= 60 - 2y + 10
= 70 - 2y
And now substituting x = 30 - y into the equation for Balloon Mania:
Total cost for Balloon Mania = 1.5y + 20
To determine which company is cheaper, we need to find when the total cost for Balloon Express is less than the total cost for Balloon Mania.
Setting up the inequality: 70 - 2y < 1.5y + 20
Simplifying the inequality: 70 - 20 < 1.5y + 2y
50 < 3.5y
y > 50/3.5
y > 14.29
Since the number of balloons must be a whole number, we round up to y = 15. Therefore, the O'Donnells should choose Balloon Mania, as it will save them $25 compared to Balloon Express.
So, the correct response is: Balloon Mania; $25.
To solve this problem using a system of linear equations, let's first define our variables:
Let x be the number of balloons ordered from Balloon Express.
Let y be the number of balloons ordered from Balloon Mania.
Now, we can set up our system of equations:
Equation 1: 2x + 10 = total cost of balloons from Balloon Express
Equation 2: 1.5y + 20 = total cost of balloons from Balloon Mania
Since the O’Donnells plan to order 30 balloons, we know that x + y = 30.
To solve the system of equations, we can use substitution or elimination.
Let's solve it using the substitution method:
From the equation x + y = 30, we can solve for x as x = 30 - y.
Substituting this value of x in Equation 1, we have: 2(30 - y) + 10 = total cost of balloons from Balloon Express
Simplifying, we get: 60 - 2y + 10 = total cost of balloons from Balloon Express
Combining like terms, we have: 2y = 70 - total cost of balloons from Balloon Express
Substituting the value of x in Equation 2, we have: 1.5y + 20 = total cost of balloons from Balloon Mania
Now we can compare the total costs of the two companies.
Since the O’Donnells plan to order 30 balloons, let's consider the case for y = 30 and calculate the total costs for each company.
For Balloon Express: 2y = 2(30) + 10 = $70
For Balloon Mania: 1.5y = 1.5(30) + 20 = $65
So, if the O’Donnells plan to order 30 balloons, they should choose Balloon Mania. By choosing Balloon Mania, they would save $5 as compared to Balloon Express.