To solve this problem, we can set up a system of equations. Let's let x be the number of balloons ordered from Balloon Express and y be the number of balloons ordered from Balloon Mania.
From the information given, we know that the O'Donnells plan to order 30 balloons, so we can write the equation:
x + y = 30
We also know that the cost for Balloon Express is $2 per balloon plus a $10 delivery fee, so the cost equation for Balloon Express is:
2x + 10 = total cost for Balloon Express
Similarly, the cost equation for Balloon Mania is:
1.50y + 20 = total cost for Balloon Mania
To determine which company the O'Donnells should choose, we need to compare the total costs. We can set up the equation:
2x + 10 = 1.50y + 20
Now, we can solve this system of equations.
First, let's solve the equation x + y = 30 for x:
x = 30 - y
Now, substitute this value for x in the cost equation for Balloon Express:
2(30 - y) + 10 = 1.50y + 20
60 - 2y + 10 = 1.50y + 20
70 - 20 = 1.50y + 2y
50 = 3.50y
y = 50/3.50
y ≈ 14.29
Since we can't order a fraction of a balloon, we'll round y down to 14. Now, substitute this value for y in the equation x = 30 - y:
x = 30 - 14
x = 16
So, the O'Donnells should order 16 balloons from Balloon Express and 14 balloons from Balloon Mania.
To find the total cost for each company, substitute the values of x and y into the cost equations:
Total cost for Balloon Express = 2(16) + 10 = $42
Total cost for Balloon Mania = 1.50(14) + 20 = $41
Therefore, the O'Donnells should choose Balloon Mania and they will save $1.
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; $5
Balloon Express; $25
Balloon Express; $5
Balloon Mania; $25
1 answer