Question

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.

Answer 1

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.