Using the systematic list, solve. Dead eye, Joe made 15 points in the basketball game. 3 points given for a long shot, 2 points given for a field goal, and 1 point is given for a free throw. How many ways can dead eye Joe score 15 points. I came up with 11. But I think I am way off
5 L
4L , 1 G , 1F
4L , 3 F
3L , 3G
3L , 2G , 2F
3L , 1G , 4F
2L , 4G , 1F
2L , 3G , 3F
2L , 2G , 5F
2L , 1G , 7F
2L , 9F
1L, 6G
1L , 5G , 2F
1L , 4G , 4F
1L , 3G , 6F
1L , 2G , 8F
1L , 1G , 10F
1L , 12F
7G , F
6G , 3F
5G , 5F
4G , 7F
3G , 9F
2G , 11F
1G , 13F
15F
think that's all ...
Wow thank you now I see the pattern
To solve this problem using a systematic list, you need to consider all the possible ways Dead Eye Joe can score 15 points by using the given point values for different shots.
To start, let's list down the possible number of long shots, field goals, and free throws Joe can make to reach a total of 15 points.
(Note: We'll denote the number of long shots as L, field goals as F, and free throws as T)
1) 3 long shots, 0 field goals, 0 free throws: (LLL)
2) 2 long shots, 2 field goals, 0 free throws: (LLFF)
3) 2 long shots, 1 field goal, 2 free throws: (LLFTT)
4) 2 long shots, 0 field goals, 4 free throws: (LLTTTT)
5) 1 long shot, 4 field goals, 0 free throws: (LFFFF)
6) 1 long shot, 3 field goals, 2 free throws: (LFFTT)
7) 1 long shot, 2 field goals, 4 free throws: (LFTTTT)
8) 1 long shot, 1 field goal, 6 free throws: (LTTTTTT)
9) 0 long shots, 6 field goals, 0 free throws: (FFFFFF)
10) 0 long shots, 5 field goals, 2 free throws: (FFTT)
11) 0 long shots, 4 field goals, 4 free throws: (FTTTTT)
Now, let's calculate the points for each scenario and check if the total is 15:
1) LLL = 3 points × 3 = 9 points
2) LLFF = 3 points × 2 + 2 points × 2 = 10 points
3) LLFTT = 3 points × 2 + 2 points × 1 + 1 point × 2 = 11 points
4) LLTTTT = 3 points × 2 + 1 point × 4 = 10 points
5) LFFFF = 3 points × 1 + 2 points × 4 = 11 points
6) LFFTT = 3 points × 1 + 2 points × 3 + 1 point × 2 = 11 points
7) LFTTTT = 3 points × 1 + 2 points × 2 + 1 point × 4 = 11 points
8) LTTTTTT = 1 point × 6 = 6 points
9) FFFFFF = 2 points × 6 = 12 points
10) FFTT = 2 points × 5 + 1 point × 2 = 12 points
11) FTTTT = 2 points × 4 + 1 point × 4 = 12 points
As you can see, none of the scenarios add up to exactly 15 points. Therefore, the number of ways Dead Eye Joe can score 15 points is zero (0).
Your initial answer of 11 was incorrect, but by going through the systematic list and calculating the points for each scenario, you can determine that there are no valid combinations that add up to 15 points.