Seth had 300 cards. ⁴₅ were pink and the rest were gold and silver. The ratio of the number of gold cards to the number of silver cards was 1 : 5. Seth decided to give away some pink cards to decrease the number of pink cards to half of the total number of cards.

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

Pink cards	Gold cards	Silver cards	Total
4x6	1x6
	1x1	5x1
24 u	1 u	5 u	300

	Pink cards	Gold cards	Silver cards
Before	24 u	1 u	5 u
Change	- ?
After	6 u	6 u
Comparing pink, gold and silver cards in the end	1	1

(a)
The total number of gold cards and silver cards is repeated. Make the total number of gold cards and silver cards the same.  LCM of 1 and 6 is 6.

Total number of cards at first
= 24 u + 1 u + 5 u
= 30 u

30 u = 300

1 u = 300 ÷ 30 = 10

Number of more pink cards than gold cards at first
= 24 u - 1 u
= 23 u
= 23 x 10
= 230

(b)
Number of more pink cards that Seth had to give away
= 24 u - 6 u
= 18 u
= 18 x 10
= 180

Answer(s): (a) 230; (b) 180