There were 209 red, green and pink pencils in a box. 13 pink pencils were removed from the box and the ratio of the number of red pencils to the number of green pencils to the number of pink pencils became 3 : 2 : 9. Then some silver pencils were added and the ratio of the number of pink pencils to the number of silver pencils was 9 : 6.

1. What was the ratio of the number of red pencils to the number of green pencils to the number of pink pencils at first?
2. How many pencils were in the box in the end?

	Red	Green	Pink	Silver	Total
Before	3 u	2 u	9 u + 13	0	209
Change 1	No change	No change	- 13		- 13
After 1	3 u	2 u	9 u		196
Change 2	No change	No change	No change	+ 6 u
After 2	3 u	2 u	9 u	6 u

(a)
Total number of pencils at first
= 3 u + 2 u + 9 u + 13
= 14 u + 13

14 u + 13 = 209
14 u = 209 - 13
14 u = 196

1 u = 196 ÷ 14 = 14

Number of red pencils at first
= 3 u
= 3 x 14
= 42

Number of green pencils at first
= 2 u
= 2 x 14
= 28

Number of pink pencils at first
= 9 u + 13
= 9 x 14 + 13
= 139 

At first
Red pencils : Green pencils : Pink pencils
42 : 28 : 139

(b)
Total number of pencils in the box in the end
= 3 u + 2 u + 9 u + 6 u
= 20 u
= 280

Answer(s): (a) 42 : 28 : 139; (b) 280