A new sport is played with teams made up of 2 forwards, 3 guards, and 1 goalie. There are 23 players available to
play forward, 21 other players available to play guard, and 9 other players available to play goalie. If the
maximum possible number of complete teams are formed, how many of the available players will not be on a
team
ans-11
the explanation says limiting factor 7 is to be multiplied by 2(forward), 3 (guards), 1 goalie. but why?? i cant understand
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- anik1989
- Students
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- Joined: Mon Apr 07, 2014 6:38 pm
- n00bpron00bpron00b
- Students
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Re: 5lb, chap 20, #28
Given:
Total no of players available to play as forward: 23
Total no of players available to play as guard: 21
Total no of players available to play as goalie: 9
Each team has the following -
Forwards : 2
Guards : 3
Goalie : 1
"Maximum possible no of complete teams that can be formed"
Case 1: If we assign 1 goalie for each team
Now, lets distribute and check for maximum possible complete teams that can be formed
Total teams will be 9
Total goalies used (1 to each team) : 9 (all used)
Total forwards used (assigning 2 to each group) - 18 (5 unused)
Total guards used (assigning 3 to each group) - 21 (all used)
If we go by the above condition of total 9 teams, the number of guards gets exhausted in the 7th team. So the last two teams will have 2 forwards, 1 goalie but no guards (we cannot consider the last 2 teams because they are not complete).
The maximum number of complete teams in this case is 7
Players unused = forwards (9) + Guards (0) + Goalie (2) = 11
Case 2:
Total guards we can pick : 21
Each team has 3 guards
So maximum complete teams that can be formed = 7
No of forwards for 7 teams (2 to each team) = 14 (unused 9)
No of guards for 7 teams (3 to each team) = 21 (all used)
No of goalies for 7 teams (1 to each team) = 7 (2 unused)
So total unused players = 9 from forwards + 0 from guard + 2 from goalie = 11
7 is the limiting factor whichever approach you decide to take.
Total no of players available to play as forward: 23
Total no of players available to play as guard: 21
Total no of players available to play as goalie: 9
Each team has the following -
Forwards : 2
Guards : 3
Goalie : 1
"Maximum possible no of complete teams that can be formed"
Case 1: If we assign 1 goalie for each team
Now, lets distribute and check for maximum possible complete teams that can be formed
Total teams will be 9
Total goalies used (1 to each team) : 9 (all used)
Total forwards used (assigning 2 to each group) - 18 (5 unused)
Total guards used (assigning 3 to each group) - 21 (all used)
If we go by the above condition of total 9 teams, the number of guards gets exhausted in the 7th team. So the last two teams will have 2 forwards, 1 goalie but no guards (we cannot consider the last 2 teams because they are not complete).
The maximum number of complete teams in this case is 7
Players unused = forwards (9) + Guards (0) + Goalie (2) = 11
Case 2:
Total guards we can pick : 21
Each team has 3 guards
So maximum complete teams that can be formed = 7
No of forwards for 7 teams (2 to each team) = 14 (unused 9)
No of guards for 7 teams (3 to each team) = 21 (all used)
No of goalies for 7 teams (1 to each team) = 7 (2 unused)
So total unused players = 9 from forwards + 0 from guard + 2 from goalie = 11
7 is the limiting factor whichever approach you decide to take.
- tommywallach
- Manhattan Prep Staff
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Re: 5lb, chap 20, #28
Great explanation, Noob!
- anik1989
- Students
- Posts: 49
- Joined: Mon Apr 07, 2014 6:38 pm
Re: 5lb, chap 20, #28
thnx. why does manhattan avoid such type clear-cut explanation?
- tommywallach
- Manhattan Prep Staff
- Posts: 1917
- Joined: Thu Mar 31, 2011 11:18 am
Re: 5lb, chap 20, #28
Our explanations are clear. You're the only person I've ever had ask about it.
-t
-t
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