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| Math Central | Quandaries & Queries |
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Question from Allen, a student: An airplane whose capacity is 100 passengers is to be chartered for a flight to Europe. The fare is to be $\$150$ per person, if 60 people buy tickets. However, the airline agrees to reduce the fare for every passenger by $\$1$ for each additional ticket sold. How many tickets should be sold to maximize the ticket revenue for this flight? |
Hi Allen,
If you are not an expert in algebra, the best way to solve this type of word problem is to first understand what’s going on by working examples.
Example 1: If 60 tickets are sold, then the revenue would be $\$150 \times 60.$
Example 2: If 61 … then $\$149 \times 61.$
Example 3: If 62 … then $\$148 \times 62.$
What do you notice about 150 + 60, 149 + 61, 148 + 62 … ?
What can you say about the largest possible value of the product $x \times y$ for two positive numbers whose sum is x + y = 210?
(Comment: It probably costs more than $\$150$ to fly to Europe if you leave from London. I wonder if there is any place from which you could fly to Europe for as little as $\$150.$)
Chris
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