Sam had 108 pens. ⁵₆ were purple and the rest were blue and brown. The ratio of the number of blue pens to the number of brown pens was 1 : 5. Sam decided to give away some purple pens to decrease the number of purple pens to half of the total number of pens.

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

Purple pens	Blue pens	Brown pens	Total
5x6	1x6
	1x1	5x1
30 u	1 u	5 u	108

	Purple pens	Blue pens	Brown pens
Before	30 u	1 u	5 u
Change	- ?
After	6 u	6 u
Comparing purple, blue and brown pens in the end	1	1

(a)
The total number of blue pens and brown pens is repeated. Make the total number of blue pens and brown pens the same.  LCM of 1 and 6 is 6.

Total number of pens at first
= 30 u + 1 u + 5 u
= 36 u

36 u = 108

1 u = 108 ÷ 36 = 3

Number of more purple pens than blue pens at first
= 30 u - 1 u
= 29 u
= 29 x 3
= 87

(b)
Number of more purple pens that Sam had to give away
= 30 u - 6 u
= 24 u
= 24 x 3
= 72

Answer(s): (a) 87; (b) 72