The total number of marbles in Bag W, Bag X and Bag Y was 160. ⁷₈ of the marbles from Bag W and 28 marbles from Bag X were removed. More marbles were then added into Bag Y until the number of marbles in it was quadrupled. The ratio of the number of marbles in Bag W to Bag X to Bag Y became 1 : 3 : 4.

1. How many less marbles were there in Bag X than Bag W at first?
2. Find the total number of marbles in Bag X and Bag Y in the end.

	Bag W	Bag X	Bag Y	Total
Before	8 u	3 u + 28	1 u	160
Change	- 7 u	- 28	+ 3 u
After	1 u		4 u
Comparing the marbles  in the end	1 u	3 u	4 u

(a)
Total number of marbles at first
= 8 u + 3 u + 28 + 1 u
= 12 u + 28

12 u + 28 = 160
12 u = 160 - 28
12 u = 132

1 u = 132 ÷ 12 = 11

Number of less marbles in Bag X than Bag W at first 
= 8 u - (3 u + 28)
= 8 u - 3 u - 28
= 5 u - 28
= 5 x 11 - 28
= 55 - 28
= 27

(b)
Total number of marbles in Bag X and Bag Y in the end
= 3 u + 4 u
= 7 u
= 7 x 11
= 77 

Answer(s): (a) 27; (b) 77