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) (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.
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