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; $5
Balloon Express; $5
Balloon Express; $25
Balloon Express; $25
Balloon Mania; $5
To solve this problem using a system of equations, we can set up the following equations:
Let x be the number of balloons ordered.
Let y be the total cost for Balloon Express.
Let z be the total cost for Balloon Mania.
For Balloon Express, the equation is: y = 2x + 10.
For Balloon Mania, the equation is: z = 1.50x + 20.
Since the O’Donnells plan to order 30 balloons, we can substitute x = 30 into the equations.
For Balloon Express: y = 2(30) + 10 = 60 + 10 = 70.
For Balloon Mania: z = 1.50(30) + 20 = 45 + 20 = 65.
Comparing the costs, the O’Donnells should choose Balloon Mania, as it will cost a total of $65, saving $5 compared to Balloon Express.
Therefore, the correct answer is: Balloon Mania; $5.
Let's set up a system of equations to solve this real-world problem.
Let's use the variable 'x' to represent the number of balloons the O'Donnells order from Balloon Express, and 'y' to represent the number of balloons they order from Balloon Mania.
The cost for Balloon Express can be expressed as:
Cost for Balloon Express = 2x + 10
The cost for Balloon Mania can be expressed as:
Cost for Balloon Mania = 1.5y + 20
The problem states that the O'Donnells plan to order a total of 30 balloons. This gives us the equation:
x + y = 30
We now have a system of equations:
1) 2x + 10 = Cost for Balloon Express
2) 1.5y + 20 = Cost for Balloon Mania
3) x + y = 30
To solve this system, we can substitute the value of (30-x) for y in equation 2, since the total balloons ordered should be 30.
1) 2x + 10 = Cost for Balloon Express
2) 1.5(30-x) + 20 = Cost for Balloon Mania
3) x + (30-x) = 30
Simplifying equation 2:
1) 2x + 10 = Cost for Balloon Express
2) 45 - 1.5x + 20 = Cost for Balloon Mania
3) x + (30-x) = 30
Simplifying equation 3:
1) 2x + 10 = Cost for Balloon Express
2) 65 - 1.5x = Cost for Balloon Mania
3) 30 = 30
Now, we can solve the system of equations.
From equation 3, we know that x = 15.
Substituting x = 15 into equation 1, we find:
2(15) + 10 = Cost for Balloon Express
30 + 10 = Cost for Balloon Express
Cost for Balloon Express = 40
Substituting x = 15 into equation 2, we find:
65 - 1.5(15) = Cost for Balloon Mania
65 - 22.5 = Cost for Balloon Mania
Cost for Balloon Mania = 42.5
Comparing the costs, we can see that the O'Donnells should choose Balloon Express, as it will cost $40, while Balloon Mania will cost $42.5.
Therefore, the O'Donnells will save $2.5 by choosing Balloon Express.
To solve this real-world problem using a system of equations, we can represent the cost for each company as variables and create an equation for each company.
Let's represent the cost for Balloon Express as "BE" and the cost for Balloon Mania as "BM".
The cost for Balloon Express can be calculated by multiplying the number of balloons by the cost per balloon and adding the delivery cost, so we have the equation:
BE = 2(30) + 10
The cost for Balloon Mania can be calculated similarly:
BM = 1.50(30) + 20
Now, let's solve these equations to find the values of BE and BM.
BE = 2(30) + 10
BE = 60 + 10
BE = 70
BM = 1.50(30) + 20
BM = 45 + 20
BM = 65
Therefore, the cost for Balloon Mania is $65 and the cost for Balloon Express is $70. The O'Donnells should choose Balloon Mania because it is cheaper.
To find out how much they will save, subtract the cost for Balloon Mania from Balloon Express:
Savings = BE - BM
Savings = 70 - 65
Savings = $5
So, the O'Donnells will save $5 by choosing Balloon Mania. The correct response is "Balloon Mania; $5"