### Problem of the Week – Answer

**Answer to the 9/24/2010 Problem of the Week**

The problem —

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?

Solution: Here is the solution, provided by the only person who got it right (name below).

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

Sharron Herring

Sharron has answered my problems many times in the past. So thanks for sharing that solution, Sharon.

Next problem will be posted this Friday, Oct. 1.