Question

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)

Answer 1

please check your answer

Answer 2

Let's use the system of equations to compare the total cost of ordering 30 balloons from both companies.

Let x be the number of balloons ordered from Balloon Express.
Let y be the number of balloons ordered from Balloon Mania.

The cost equation for Balloon Express is: Cx = 2x + 10
The cost equation for Balloon Mania is: Cy = 1.50y + 20

Given that the O'Donnells plan to order a total of 30 balloons, we have the equation: x + y = 30

We want to find out which company the O'Donnells should choose based on the total cost. So, we need to find the values of x and y that minimizes the total cost.

Substitute x = 30 - y into the cost equation for Balloon Express and Balloon Mania:

Cx = 2(30 - y) + 10 = 60 - 2y + 10 = 70 - 2y
Cy = 1.50y + 20

Now, set both equations equal to each other to find the point at which the cost of both companies is equal:

70 - 2y = 1.50y + 20
70 - 20 = 1.50y + 2y
50 = 3.50y
y = 50 / 3.50
y = 14.29...

Since you can't order a fraction of a balloon, we can conclude that y = 14.

Now, plug in y = 14 into x + y = 30 to find x:
x + 14 = 30
x = 30 - 14
x = 16

Therefore, the O'Donnells should order 16 balloons from Balloon Express and 14 balloons from Balloon Mania to minimize cost.

Total cost from Balloon Express = 70 - 2(14) = $42
Total cost from Balloon Mania = 1.50(14) + 20 = $40

Therefore, the O'Donnells should choose Balloon Mania because they will save $2 by ordering from that company.

Answer 3

Apologies for the error in the previous response. Let's correct the calculation and find the right answer.

Given:
Balloon Express: $2 per balloon + $10 for delivery
Balloon Mania: $1.50 per balloon + $20 for delivery

Let x be the number of balloons ordered from Balloon Express
Let y be the number of balloons ordered from Balloon Mania

The total cost for Balloon Express: Cx = 2x + 10
The total cost for Balloon Mania: Cy = 1.50y + 20

Given that x + y = 30 (total balloons ordered)

We need to compare the total costs and determine which company the O'Donnells should choose:

Cost for Balloon Express: Cx = 2x + 10
Cost for Balloon Mania: Cy = 1.50y + 20

Now, we substitute y = 30 - x into the cost equation for Balloon Express:

Cx = 2x + 10

Substitute y = 30 - x into the cost equation for Balloon Mania:

Cy = 1.50(30 - x) + 20
Cy = 45 - 1.50x + 20
Cy = 65 - 1.50x

Now, equate the two cost equations:

2x + 10 = 65 - 1.50x
2x + 1.50x = 65 - 10
3.50x = 55
x = 55 / 3.50
x = 15.71...

Since the number of balloons must be a whole number, x = 16.

Now, calculate the number of balloons ordered at Balloon Mania:

y = 30 - 16
y = 14

Therefore, the O'Donnells should order 16 balloons from Balloon Express and 14 balloons from Balloon Mania.

Total cost from Balloon Express: Cx = 2(16) + 10 = $42
Total cost from Balloon Mania: Cy = 1.50(14) + 20 = $41

The O'Donnells should choose Balloon Mania because they will save $1 by ordering from that company.