Rael had 210 pens. ⁵₇ were white and the rest were brown and pink. The ratio of the number of brown pens to the number of pink pens was 1 : 5. Rael decided to give away some white pens to decrease the number of white pens to half of the total number of pens.

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

White pens	Brown pens	Pink pens	Total
5x3	2x3
	1x1	5x1
15 u	1 u	5 u	210

	White pens	Brown pens	Pink pens
Before	15 u	1 u	5 u
Change	- ?
After	6 u	6 u
Comparing white, brown and pink pens in the end	1	1

(a)
The total number of brown pens and pink pens is repeated. Make the total number of brown pens and pink pens the same.  LCM of 2 and 6 is 6.

Total number of pens at first
= 15 u + 1 u + 5 u
= 21 u

21 u = 210

1 u = 210 ÷ 21 = 10

Number of more white pens than brown pens at first
= 15 u - 1 u
= 14 u
= 14 x 10
= 140

(b)
Number of more white pens that Rael had to give away
= 15 u - 6 u
= 9 u
= 9 x 10
= 90

Answer(s): (a) 140; (b) 90