Question

in the second half of the game, the Wildcats again scored 18 points. This time, however, we don't know how many total shots were made. List all of the possible combinations of 2- and 3- point shots that could total 18 points. include a sentence explain how you know that you found all of the possible answers. please help me answer this would really appreciate it.

Answer 1

Lets start with the chain of 3's:

18 = 3 + 3 + 3 + 3 + 3 + 3          

But, we know that

3 + 3 = 2 + 2 + 2

Sol, let's replace 3 + 3 by 2 + 2 + 2 one by one.

Hence, the possible ways of combinations are listed below:

18 = 3 + 3 + 3 + 3 + 2 + 2 + 2                        (1)

18 = 3 + 3 + 2 + 2 + 2 + 2 + 2 + 2                  (2)

Therefore, there are two combinations of 2- and 3- point shots that could total 18 points.