SOLUTION: A club can elect a member as president and another member as treasurer in 506 different ways. How many members does the club have?

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Question 896212: A club can elect a member as president and another member as treasurer in 506 different ways. How many members does the club have?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's say we had x members total

That means we have x choices for president (assuming they are all candidates).

That leaves us with x-1 choices for treasurer. We cannot pick the same person to run both positions.

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So we have x*(x-1) ways to pick 2 people (from a pool of x people)

We know that there are 506 ways to do this, so x*(x-1) = 506

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Solve for x

x*(x-1) = 506

x^2-x = 506

x^2-x-506 = 0

Use the quadratic formula to get the solutions x = 23 or x = -22.

I show the steps in solving here.

x is the number of people, so it has to be a positive whole number. That means we ignore x = -22

The only practical solution is x = 23.

That means the club has 23 members.

Notice how

x*(x-1) = 506

23*(23-1) = 506

23*22 = 506

506 = 506

So that confirms the answer.