Ratio of Marbles of
May, Teddy, Sam
3 : 5 : 2
Lets name the ratio as Bags of Marbles

May lost half her total Bags of Marbles to Teddy,
Half of 3 Bags is 1.5 Bags

New Ratio of Bags of Marbles now is
May, Teddy, Sam
1.5 : 6.5 : 2

Teddy later on lost 65 Marbles to Sam.
Teddy's Total Marbles: 6.5 Bags - 65 Marbles

Sam Won 65 Marbles from Teddy.
Sam's Total Marbles: 2 Bags + 65 Marbles = ?

Sam had 3 times as many marbles as May After Winning 65 Marbles from Teddy.
May's Total Marbles: 1.5 Bags
Sam's Total Marbles: 1.5 Bags x 3 = 4.5 Bags
Sam's Total Marbles: 2 Bags + 65 Marbles = 4.5 Bags

So the addition of 2.5 Bags is equals to 65 marbles.

Find Out How Many Marbles are in 1 Bag.
65 Marbles is shared inside 2.5 Bags
65 / 2.5 = 26 Marbles
1 Bag of Marbles = 26 Marbles

(a) Percentage Increase in Sam's Marble
First, Find How Many Bags is Equals to 100%
May + Teddy + Sam = 100%
3 : 5 : 2
3 + 5 + 2 = 10 Bags
10 Bags = 100%
1 Bag = 10%
26 Marbles = 10%
Sam Increased by 65 Marbles,
Since 26 Marbles is 10%
Find out how many % is 65 Marbles,
65/26 x 10% = 25%
65 Marbles is 25%

Percentage increase is 25%

(b) Teddy's Marble at the end of the game
6.5Bags - 65 Marbles
Since 1 Bag = 26 Marbles
6.5 x 26 = 169 Marbles
169 Marbles - 65 Marbles = 104 Marbles.

Teddy Have 104 Marbles at the end of the game.

This is also my preliminary exam this year