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)%0D%0AResponses%0D%0A%0D%0ABalloon Express; $25%0D%0ABalloon Express; $25%0D%0A%0D%0ABalloon Mania; $5%0D%0ABalloon Mania; $5%0D%0A%0D%0ABalloon Express; $5 %0D%0ABalloon Express; $5 %0D%0A%0D%0ABalloon Mania; $25

Answer 1

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

The cost for Balloon Express is: 2x + 10
The cost for Balloon Mania is: 1.5y + 20

We know that the total number of balloons ordered is 30, so:
x + y = 30

We also know that the O’Donnells plan to order 30 balloons, so:
x + y = 30

We can now solve this system of equations to find the value of x and y. Subtracting the second equation from the first equation, we get:

2x + 10 - (1.5y + 20) = 0

2x + 10 - 1.5y - 20 = 0

2x -1.5y - 10 = 0

2x - 1.5y = 10

Rearranging the first equation, we get:

x = 30 - y

Now we substitute this value of x into the second equation:

2(30 - y) - 1.5y = 10

60 - 2y - 1.5y = 10

-3.5y = -50

y = 14.2857

Now substitute this value of y into the expression for x:

x = 30 - 14.2857

x = 15.7143

So the O’Donnells should choose Balloon Express and they will save $25.