let the score in the first game be m and in the second be n.
we know that the total score is 35
this means that: m+n=35 .....> equation I
she scored in the second games 6 times as many as in the first one
this means that: n=6m .......> equation II
substitute with equation II in I:
m+6m=35
7m=35
m=5
therefore,
she scored 5 in the first game and 30 in the second one
this means that she scored 30-5=25 points in the second game more than in the first one