Cml

[17rkearns]

I have a Continental Math League Problem that I can't figure out at all!
These are them:
48.) Fran and Dan are members of the school's chess team. Dan played in 1 out of ever 3 games. Fran, who played more games played in 12 games. What is the largest number of games the team could have played?

I know this has something to do with the fraction 1/3 and a chart of some sort.
Please help!
Thanks!

 

[Deleted member 4993]

I have a Continental Math League Problem that I can't figure out at all!
These are them:
48.) Fran and Dan are members of the school's chess team. Dan played in 1 out of ever 3 games. Fran, who played more games played in 12 games. What is the largest number of games the team could have played?

I know this has something to do with the fraction 1/3 and a chart of some sort.
Please help!
Thanks!

What is the maximum number of games that Dan could have participated in this particular situation?

If that is 1 of 3 of total games - what would be the maximum number of (total) games?

 

[17rkearns]

So I would take the 1/3 games. and take 12 and divide it by 3 to get 4. Then I would add the four to the 12 games that Fran played. Right?

 

[tkhunny]

I have to wonder why you think this problem is all that different from others you have faced.

Let's write down what we know (given) and see what we can conclude.

N = Total Games Played
D = Dan's Games = N/3
F = Fran's Games = 12 > D

This narrows Dan's games down to 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11

At this point, we may notice that N > 12, so D = N/3 > 4

This narrows Dan's games down to 5, 6, 7, 8, 9, 10, 11

A little more thought might produce N > F + D = 12 + N/3, Giving (2/3)N > 12 or N > 18

This narrows Dan's games down to 7, 8, 9, 10, 11

Of course, at some point we should realize that we are interested in only the MAXIMUM number. All this fuss about lesser values might be an interesting exercize, but doesn't much get us to the answer to this question.