During a game, players can win and lose counters. at the start of the game
rob, tim and zak share the counters in the ratio 5 : 6 : 7 at the end of the game
rob, tim and zak share the same number of counters in the ratio 7 : 9 : 8 show that rob ends the game with more counters than he started with.

The first step is to calculate what fraction of the counters that Rob has.

Add all the portions together to find the total: 5+6+7= 18
Rob has 5 out of the 18, or 5/18, or 0.278

Next, do the same for the end ratio:
7+9+8= 24 and Rob has 7/24, or 0.292

By comparing his beginning portion (0.278) to his end portion (0.292) it is clear that he has a greater portion of the total counters. Given that the problem states that the number of counters stays the same, Rob must have more counters than he started with.

Sin(a)+cos(a)+cot(a)-1=2(csc(x)+1)