George had 108 pencils. ⁵₆ were yellow and the rest were pink and brown. The ratio of the number of pink pencils to the number of brown pencils was 1 : 2. George decided to give away some yellow pencils to decrease the number of yellow pencils to half of the total number of pencils.

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

Yellow pencils	Pink pencils	Brown pencils	Total
5x3	1x3
	1x1	2x1
15 u	1 u	2 u	108

	Yellow pencils	Pink pencils	Brown pencils
Before	15 u	1 u	2 u
Change	- ?
After	3 u	3 u
Comparing yellow, pink and brown pencils in the end	1	1

(a)
The total number of pink pencils and brown pencils is repeated. Make the total number of pink pencils and brown pencils the same.  LCM of 1 and 3 is 3.

Total number of pencils at first
= 15 u + 1 u + 2 u
= 18 u

18 u = 108

1 u = 108 ÷ 18 = 6

Number of more yellow pencils than pink pencils at first
= 15 u - 1 u
= 14 u
= 14 x 6
= 84

(b)
Number of more yellow pencils that George had to give away
= 15 u - 3 u
= 12 u
= 12 x 6
= 72

Answer(s): (a) 84; (b) 72