## Kiss those Math Headaches GOODBYE!

### Problem of the Week — 9/24/2010

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.

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:

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

Backgammon, Image via Wikipedia

#### Comments on: "Problem of the Week — 9/24/2010" (1)

1. Sharron Herring said:

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

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