Question 203414
Let's assume that the five players are called A, B, C, D, and E and that they are listed in increasing numerical sequence of the points scored.
So, A = Amanda who scored the fewest points and she had to have scored at least 10 points. 
B = Kara who scored 16 points.
The others we don't know yet. So we can write:
{{{(10+16+C+D+E)/5 = 16}}} because the average score is 16 and each player scored more than 9 points.
Multiply both sides by 5.
{{{(26+C+D+E) = 80}}} Subtract 26 from both sides.
{{{C+D+E = 54}}} Now we know that each player scored a different number of points, so player C must have scored at least 17 points and let's assume that players D and E scored 1 point more than the previous player, so we get:
{{{(17+18+19) = 54}}} Hopefully?
{{{54 = 54}}} Bingo!
So we can say that Amanda scored 10 points!
Let's check:
{{{(10+16+17+18+19)/5 = 80/5}}}={{{16}}} OK!