Question

A basketball team recently scored a total of 81 points on a combination of​ 2-point field​ goals, 3-point field​ goals, and​ 1-point foul shots.​ Altogether, the team made 47 baskets and 15 more​ 2-pointers than foul shots. How many shots of each kind were​ made?

Answer 1

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