**Problem of the Week — 9/24/2010**

At Gamesville High, students love their clubs. While 20% of the children in the Hex Club are also members of the Backgammon Club, 80% of children in the Backgammon Club are also members of the Hex Club. The Backgammon Club has 35 children. The question: how many children are in the Hex Club?

To get the honor of being put into the Winner’s Circle, you need to get the correct answer and show how you arrived at it.

Please write your answers as comments on the blog post. Or alternatively, you can send it as an email to me: josh@SingingTurtle.com

I will post the answer and name the five who make it to the Winner’s Circle on Monday.

P.S.: Hex is a great board game, invented by two mathematicians. If you’d like to read a post about it, go here:

http://mathchat.wordpress.com/2010/01/27/play-a-game-meet-john-nash/

Hi Josh,

20%=0.2, 80%= 0.8.

Let X = the number of students in the Hex Club

Let Y = the number of students in the Backgammon Club

So:

0.2X=0.8 Y because the 20% and 80% are the same children, the same number of people. It just looks different because the percentages show a relationship between the total numbers in each club.

Speaking of total numbers, the problem tells us how many are in the Backgammon Club: 35. So:

Y=35

We now have two equations. We can substitute the value of Y from the second for the Y in the first and solve for X.

0.2X=0.8 (35)

0.2X=28

X=140

There are 140 students in the Hex Club