Luis had 264 pencils. ⁵₆ were green and the rest were blue and red. The ratio of the number of blue pencils to the number of red pencils was 1 : 3. Luis decided to give away some green pencils to decrease the number of green pencils to half of the total number of pencils.

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

Green pencils	Blue pencils	Red pencils	Total
5x4	1x4
	1x1	3x1
20 u	1 u	3 u	264

	Green pencils	Blue pencils	Red pencils
Before	20 u	1 u	3 u
Change	- ?
After	4 u	4 u
Comparing green, blue and red pencils in the end	1	1

(a)
The total number of blue pencils and red pencils is repeated. Make the total number of blue pencils and red pencils the same.  LCM of 1 and 4 is 4.

Total number of pencils at first
= 20 u + 1 u + 3 u
= 24 u

24 u = 264

1 u = 264 ÷ 24 = 11

Number of more green pencils than blue pencils at first
= 20 u - 1 u
= 19 u
= 19 x 11
= 209

(b)
Number of more green pencils that Luis had to give away
= 20 u - 4 u
= 16 u
= 16 x 11
= 176

Answer(s): (a) 209; (b) 176