SOLUTION: A group of 20 senior citizens can charter a bus for a one-day excursion trip for $15 per person. The charter company agrees to reduce the price of each ticket by 10¢ for each addi

Question 1207800: A group of 20 senior citizens can charter a bus for a one-day excursion trip for $15 per person. The charter company agrees to reduce the price of each ticket by 10¢ for each additional passenger in excess of 20 who goes on the trip, up to a maximum of 44 passengers (the capacity of the bus). If the final bill from the charter company was $482.40,how many seniors went on the trip, and how much did each pay?
This is too wordy for me to even know where to begin.

Answer by greenestamps(13195) (Show Source): You can put this solution on YOUR website!

Unless you have a lot of experience, start by defining a variable.

What does the problem ask for? It asks for the number of seniors who went on the trip.

We could let x be the number who went on the trip. But then the number of ADDITIONAL seniors, after the original 20, would be (x-20), which would complicate the solution process.

Since the price per senior decreases by 10 cents for each ADDITIONAL senior....

Let x = number of additional seniors

The total cost of the trip, $482.40, is the product of the number of seniors and the cost for each. Using our definition of x...

20+x = number of seniors
15-0.1x = cost per senior (writing 10 cents as 0.1 dollars)

Then

[1]

Expand using FOIL...

This is an ugly quadratic equation that you could solve by factoring, by using the quadratic formula, or by using a tool like a graphing calculator. Note that since a purely algebraic solution is not easy, the problem can probably be solved most quickly using a graphing calculator to solve equation [1] directly.

In any case....

Factoring gives

So the number of additional seniors is either 114 or 16. But since the capacity of the bus is 44, the correct number of additional seniors is 16.

ANSWERS:
number of seniors who went on the trip: 20+x = 20+16 = 36
cost each: 15-0.1x =15-0.1(16) = $15.00-$1.60 = $13.40
CHECK: 36($13.40) = $482.40

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