Vanessa had some blue stamps and grey stamps in 2 boxes. In Box E, the ratio of the number of blue stamps to grey stamps was 10 : 7. In Box F, the number of blue stamps was 2 times the number of grey stamps. Vanessa transferred ⁴₇ of the grey stamps from Box E to Box F. The number of stamps in Box E became 39 and the ratio of the number of blue stamps to grey stamps in Box F became 4 : 5.

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

	Box E		Box F
	Blue	Grey	Blue	Grey
Comparing blue stamps and grey stamps at first	10 u	7 u	2x2 = 4 p	1x2 = 2 p
Before		7 u
Change		- 4 u		+ 4 u
After		3 u
Comparing blue stamps and grey stamps in the end	10 u	3 u	4 p	5 p

(a)
Total number of stamps in the end for Box E
= 10 u + 3 u
= 13 u

13 u = 39

1 u = 39 ÷ 13 = 3

Number of grey stamps that were transferred from Box E to Box F
= 4 u
= 4 x 3
= 12

(b)
The number of blue stamps in Box F remains unchanged.  Make the number of blue stamps in Box F the same.  LCM of 2 and 4 is 4. 

Increase in the number of grey stamps in Box F
= 5 p - 2 p
= 3 p

3 p = 4 u
3 p = 12

1 p = 12 ÷ 3 = 4

Number of stamps in Box F in the end
= 4 p + 5 p
= 9 p
= 9 x 4
= 36

Answer(s): (a) 12; (b) 36