Bobby had 120 cards. ³₅ were white and the rest were green and gold. The ratio of the number of green cards to the number of gold cards was 1 : 2. Bobby decided to give away some white cards to decrease the number of white cards to half of the total number of cards.

1. How many more white cards than green cards did he have at first?
2. How many white cards did he have to give away?

White cards	Green cards	Gold cards	Total
3x3	2x3
	1x2	2x2
9 u	2 u	4 u	120

	White cards	Green cards	Gold cards
Before	9 u	2 u	4 u
Change	- ?
After	6 u	6 u
Comparing white, green and gold cards in the end	1	1

(a)
The total number of green cards and gold cards is repeated. Make the total number of green cards and gold cards the same.  LCM of 2 and 3 is 6.

Total number of cards at first
= 9 u + 2 u + 4 u
= 15 u

15 u = 120

1 u = 120 ÷ 15 = 8

Number of more white cards than green cards at first
= 9 u - 2 u
= 7 u
= 7 x 8
= 56

(b)
Number of more white cards that Bobby had to give away
= 9 u - 6 u
= 3 u
= 3 x 8
= 24

Answer(s): (a) 56; (b) 24