Nora had some purple beads and grey beads in 2 boxes. In Box E, the ratio of the number of purple beads to grey beads was 9 : 5. In Box F, the number of purple beads was 2 times the number of grey beads. Nora transferred ²₅ of the grey beads from Box E to Box F. The number of beads in Box E became 48 and the ratio of the number of purple beads to grey beads in Box F became 6 : 7.

1. How many grey beads were transferred from Box E to Box F?
2. What was the number of beads in Box F after the transfer?

	Box E		Box F
	Purple	Grey	Purple	Grey
Comparing purple beads and grey beads at first	9 u	5 u	2x3 = 6 p	1x3 = 3 p
Before		5 u
Change		- 2 u		+ 2 u
After		3 u
Comparing purple beads and grey beads in the end	9 u	3 u	6 p	7 p

(a)
Total number of beads in the end for Box E
= 9 u + 3 u
= 12 u

12 u = 48

1 u = 48 ÷ 12 = 4

Number of grey beads that were transferred from Box E to Box F
= 2 u
= 2 x 4
= 8

(b)
The number of purple beads in Box F remains unchanged.  Make the number of purple beads in Box F the same.  LCM of 2 and 6 is 6. 

Increase in the number of grey beads in Box F
= 7 p - 3 p
= 4 p

4 p = 2 u
4 p = 8

1 p = 8 ÷ 4 = 2

Number of beads in Box F in the end
= 6 p + 7 p
= 13 p
= 13 x 2
= 26

Answer(s): (a) 8; (b) 26