Xuan had some red cards and brown cards in 2 packets. In Packet N, the ratio of the number of red cards to brown cards was 10 : 3. In Packet P, the number of red cards was 2 times the number of brown cards. Xuan transferred ²₃ of the brown cards from Packet N to Packet P. The number of cards in Packet N became 88 and the ratio of the number of red cards to brown cards in Packet P became 6 : 7.

1. How many brown cards were transferred from Packet N to Packet P?
2. What was the number of cards in Packet P after the transfer?

	Packet N		Packet P
	Red	Brown	Red	Brown
Comparing red cards and brown cards at first	10 u	3 u	2x3 = 6 p	1x3 = 3 p
Before		3 u
Change		- 2 u		+ 2 u
After		1 u
Comparing red cards and brown cards in the end	10 u	1 u	6 p	7 p

(a)
Total number of cards in the end for Packet N
= 10 u + 1 u
= 11 u

11 u = 88

1 u = 88 ÷ 11 = 8

Number of brown cards that were transferred from Packet N to Packet P
= 2 u
= 2 x 8
= 16

(b)
The number of red cards in Packet P remains unchanged.  Make the number of red cards in Packet P the same.  LCM of 2 and 6 is 6. 

Increase in the number of brown cards in Packet P
= 7 p - 3 p
= 4 p

4 p = 2 u
4 p = 16

1 p = 16 ÷ 4 = 4

Number of cards in Packet P in the end
= 6 p + 7 p
= 13 p
= 13 x 4
= 52

Answer(s): (a) 16; (b) 52