If I am reading your question correctly... you forgot the "MORE THAN" in the third game.
So you have games ____ , ____ , _____ and three
the second game the team scored 23 points... _____, __23__, ___
The first game was 17 more than the third game (so the third game is x)
x+17 + 23 + x < 60
..... you should end up with x <10 so that means that in the first game they scored x + 17, and x must be less than 10. So the greatest number of points in game one would occur when x is the closest whole number to 10 (so when it is 9)
x + 17
9 + 17
= 26
So the most points that could have been scored in game 1 is 26 :)