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

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.