Xandra had some brown beads and gold beads in 2 boxes. In Box A, the ratio of the number of brown beads to gold beads was 9 : 5. In Box B, the number of brown beads was 4 times the number of gold beads. Xandra transferred ³₅ of the gold beads from Box A to Box B. The number of beads in Box A became 77 and the ratio of the number of brown beads to gold beads in Box B became 8 : 9.

1. How many gold beads were transferred from Box A to Box B?
2. What was the number of beads in Box B after the transfer?

	Box A		Box B
	Brown	Gold	Brown	Gold
Comparing brown beads and gold beads at first	9 u	5 u	4x2 = 8 p	1x2 = 2 p
Before		5 u
Change		- 3 u		+ 3 u
After		2 u
Comparing brown beads and gold beads in the end	9 u	2 u	8 p	9 p

(a)
Total number of beads in the end for Box A
= 9 u + 2 u
= 11 u

11 u = 77

1 u = 77 ÷ 11 = 7

Number of gold beads that were transferred from Box A to Box B
= 3 u
= 3 x 7
= 21

(b)
The number of brown beads in Box B remains unchanged.  Make the number of brown beads in Box B the same.  LCM of 4 and 8 is 8. 

Increase in the number of gold beads in Box B
= 9 p - 2 p
= 7 p

7 p = 3 u
7 p = 21

1 p = 21 ÷ 7 = 3

Number of beads in Box B in the end
= 8 p + 9 p
= 17 p
= 17 x 3
= 51

Answer(s): (a) 21; (b) 51