Xuan had some white beads and gold beads in 2 bags. In Bag T, the ratio of the number of white beads to gold beads was 7 : 5. In Bag U, the number of white beads was 2 times the number of gold beads. Xuan transferred ³₅ of the gold beads from Bag T to Bag U. The number of beads in Bag T became 36 and the ratio of the number of white beads to gold beads in Bag U became 6 : 7.

1. How many gold beads were transferred from Bag T to Bag U?
2. What was the number of beads in Bag U after the transfer?

	Bag T		Bag U
	White	Gold	White	Gold
Comparing white beads and gold beads at first	7 u	5 u	2x3 = 6 p	1x3 = 3 p
Before		5 u
Change		- 3 u		+ 3 u
After		2 u
Comparing white beads and gold beads in the end	7 u	2 u	6 p	7 p

(a)
Total number of beads in the end for Bag T
= 7 u + 2 u
= 9 u

9 u = 36

1 u = 36 ÷ 9 = 4

Number of gold beads that were transferred from Bag T to Bag U
= 3 u
= 3 x 4
= 12

(b)
The number of white beads in Bag U remains unchanged.  Make the number of white beads in Bag U the same.  LCM of 2 and 6 is 6. 

Increase in the number of gold beads in Bag U
= 7 p - 3 p
= 4 p

4 p = 3 u
4 p = 12

1 p = 12 ÷ 4 = 3

Number of beads in Bag U in the end
= 6 p + 7 p
= 13 p
= 13 x 3
= 39

Answer(s): (a) 12; (b) 39