SOLUTION: A hockey game between two teams is 'relatively close' if the number of goals scored by the two teams never differ by more than 2. In how many ways can the first 12 goals of a game

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Question 1182799: A hockey game between two teams is 'relatively close' if the number of goals scored by the two teams never differ by more than 2. In how many ways can the first 12 goals of a game be scored if the game is 'relatively close'?
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
system%28x%2By=12%2Cabs%28x-y%29%3C=2%29

y = 12-x

|x-(12-x)| ≤ 2

|x-12+x| ≤ 2

|2x-12| ≤ 2

2|x-6| ≤ 2

|x-6| ≤ 1

-1 ≤ x-6 ≤ 1
+6    +6  +6
------------
 5 ≤ x   ≤ 7

x = 5,6,7   
y = 7,6,5

3 ways.

Edwin

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The other tutor misread and/or misunderstood the problem.

Re-post if you want to try to get help with this.

I have seen this type of problem before, but at the moment I can't recall the solution method, so I can't help right now. But I will continue thinking about the problem to see if I can remember....