Kathy had some silver stamps and blue stamps in 2 bags. In Bag M, the ratio of the number of silver stamps to blue stamps was 10 : 7. In Bag N, the number of silver stamps was 2 times the number of blue stamps. Kathy transferred ³₇ of the blue stamps from Bag M to Bag N. The number of stamps in Bag M became 112 and the ratio of the number of silver stamps to blue stamps in Bag N became 6 : 7.

1. How many blue stamps were transferred from Bag M to Bag N?
2. What was the number of stamps in Bag N after the transfer?

	Bag M		Bag N
	Silver	Blue	Silver	Blue
Comparing silver stamps and blue stamps at first	10 u	7 u	2x3 = 6 p	1x3 = 3 p
Before		7 u
Change		- 3 u		+ 3 u
After		4 u
Comparing silver stamps and blue stamps in the end	10 u	4 u	6 p	7 p

(a)
Total number of stamps in the end for Bag M
= 10 u + 4 u
= 14 u

14 u = 112

1 u = 112 ÷ 14 = 8

Number of blue stamps that were transferred from Bag M to Bag N
= 3 u
= 3 x 8
= 24

(b)
The number of silver stamps in Bag N remains unchanged.  Make the number of silver stamps in Bag N the same.  LCM of 2 and 6 is 6. 

Increase in the number of blue stamps in Bag N
= 7 p - 3 p
= 4 p

4 p = 3 u
4 p = 24

1 p = 24 ÷ 4 = 6

Number of stamps in Bag N in the end
= 6 p + 7 p
= 13 p
= 13 x 6
= 78

Answer(s): (a) 24; (b) 78