Charlie had 100 pens. ⁴₅ were gold and the rest were silver and purple. The ratio of the number of silver pens to the number of purple pens was 1 : 3. Charlie decided to give away some gold pens to decrease the number of gold pens to half of the total number of pens.

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

Gold pens	Silver pens	Purple pens	Total
4x4	1x4
	1x1	3x1
16 u	1 u	3 u	100

	Gold pens	Silver pens	Purple pens
Before	16 u	1 u	3 u
Change	- ?
After	4 u	4 u
Comparing gold, silver and purple pens in the end	1	1

(a)
The total number of silver pens and purple pens is repeated. Make the total number of silver pens and purple pens the same.  LCM of 1 and 4 is 4.

Total number of pens at first
= 16 u + 1 u + 3 u
= 20 u

20 u = 100

1 u = 100 ÷ 20 = 5

Number of more gold pens than silver pens at first
= 16 u - 1 u
= 15 u
= 15 x 5
= 75

(b)
Number of more gold pens that Charlie had to give away
= 16 u - 4 u
= 12 u
= 12 x 5
= 60

Answer(s): (a) 75; (b) 60