Olivia had 140 cards. ²₇ were silver and the rest were gold and black. The ratio of the number of gold cards to the number of black cards was 1 : 3. Olivia decided to buy some more silver cards to increase the number of silver cards to half of the total number of cards.

1. How many less gold cards than silver cards did he have at first?
2. How many more silver cards did he have to buy?

Silver cards	Gold cards	Black cards	Total
2x4	5x4
	1x5	3x5
8 u	5 u	15 u	140

	Silver cards	Gold cards	Black cards
Before	8 u	5 u	15 u
Change	+ ?
After	20 u	20 u
Comparing silver, gold and black cards in the end	1	1

(a)
The total number of gold cards and black cards is repeated. Make the total number of gold cards and black cards the same.  LCM of 5 and 4 is 20.

Total number of cards at first
= 8 u + 5 u + 15 u
= 28 u

28 u = 140

1 u = 140 ÷ 28 = 5

Number of less gold cards than silver cards at first
= 8 u - 5 u
= 3 u
= 3 x 5
= 15

(b)
Number of more silver cards that Olivia had to buy
= 20 u - 8 u
= 12 u
= 12 x 5
= 60

Answer(s): (a) 15; (b) 60