Solve this real world problem using a system of equations. The O'Donnells are having a 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. The O'Donnell's plan to order 30 balloons, which company should they choose and how much will they save? A. Balloon mania $25? B. Balloon Express $5 c. Balloon mania $5 d. Balloon Express $25
Let's denote the number of balloons from Balloon Express as x and the number of balloons from Balloon Mania as y.
According to the given information:
Balloon Express charges $2 per balloon and $10 for delivery, so the total cost from Balloon Express is 2x + 10.
Balloon Mania charges $1.50 per balloon and $20 for delivery, so the total cost from Balloon Mania is 1.50y + 20.
The O'Donnells plan to order 30 balloons, so we have x + y = 30.
To determine which company they should choose, we need to find the solution to the system of equations.
Now we will substitute y = 30 - x into the total cost from Balloon Express equation:
Total cost from Balloon Express = 2x + 10
= 2(30 - x) + 10
= 60 - 2x + 10
= 70 - 2x
Total cost from Balloon Mania = 1.50y + 20
= 1.50(30 - x) + 20
= 45 - 1.50x + 20
= 65 - 1.50x
So the system of equations becomes:
70 - 2x = 65 - 1.50x
Now we will solve for x:
70 - 2x = 65 - 1.50x
2x - 1.50x = 70 - 65
0.50x = 5
x = 5 / 0.50
x = 10
Substituting this value of x back into the equation y = 30 - x, we find y = 20.
This means that the O'Donnells should choose Balloon Express, and they will save $5 compared to Balloon Mania.
Therefore, the correct answer is: C. Balloon mania $5.