Emma had some blue cards and white cards in 2 bags. In Bag U, the ratio of the number of blue cards to white cards was 7 : 5. In Bag V, the number of blue cards was 4 times the number of white cards. Emma transferred ³₅ of the white cards from Bag U to Bag V. The number of cards in Bag U became 126 and the ratio of the number of blue cards to white cards in Bag V became 8 : 9.

1. How many white cards were transferred from Bag U to Bag V?
2. What was the number of cards in Bag V after the transfer?

	Bag U		Bag V
	Blue	White	Blue	White
Comparing blue cards and white cards at first	7 u	5 u	4x2 = 8 p	1x2 = 2 p
Before		5 u
Change		- 3 u		+ 3 u
After		2 u
Comparing blue cards and white cards in the end	7 u	2 u	8 p	9 p

(a)
Total number of cards in the end for Bag U
= 7 u + 2 u
= 9 u

9 u = 126

1 u = 126 ÷ 9 = 14

Number of white cards that were transferred from Bag U to Bag V
= 3 u
= 3 x 14
= 42

(b)
The number of blue cards in Bag V remains unchanged.  Make the number of blue cards in Bag V the same.  LCM of 4 and 8 is 8. 

Increase in the number of white cards in Bag V
= 9 p - 2 p
= 7 p

7 p = 3 u
7 p = 42

1 p = 42 ÷ 7 = 6

Number of cards in Bag V in the end
= 8 p + 9 p
= 17 p
= 17 x 6
= 102

Answer(s): (a) 42; (b) 102