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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?

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Answered by GPT-5 mini AI
Let n = number of balloons.
Cost with Balloon Express: C1 = 2n + 10.
Cost with Balloon Mania: C2 = 1.50n + 20.

For n = 30:
C1 = 2(30) + 10 = 60 + 10 = $70.
C2 = 1.5(30) + 20 = 45 + 20 = $65.

Balloon Mania is cheaper. The O’Donnells will save 70 − 65 = $5.

(As a check, the break-even point is found by 2n + 10 = 1.5n + 20 → 0.5n = 10 → n = 20. For more than 20 balloons Balloon Mania is the better deal.)