Answer: 1-p --- 15 shots;
2-p --- 30 shots;
3-p --- 2 shots
Explanation: If we start from the given data, that 15 more 2-pointer shots (field goals) than 1-pointer foul shots and there were 47 baskets in total, then with x we can represent number of 1-p fouls shots and with (x + 15) number of 2-p field shots. Then the number of 3-p field shots can be found from the equation 3-p = 47 - x - (x + 15) = 32 - 2·x
1-p --- x
2-p --- x + 15
3-p --- 32 - x
If we know that a total of 81 points have been scored, so no shots, then the following equation can be set
1·x + 2·(x + 15) + 3·(32 - 2·x) = 81
3·x + 30 + 96 - 6·x = 81
126 - 3·x = 81
45 = 3·x ⇒ x = 15, means the number of shots for 1-p is 15.
The number of shots for 2-p and 3-p can also be found as follows:
2-p ---- x + 15 = 15 + 15 = 30
3-p ---- 32 - 2·x = 32 - 2·30 = 32 - 30 = 2
Check: total number of shots: 1-p 15 + 2-p 30 + 3-p 2 = 47 number of shots (baskets).
Also check: total number of points: 15 fouls shots points + 60 field 2-p points + 6 field 3-p points = 15 + 60 + 6 = 81
