There were 216 grey, purple and yellow pencils in a box. 12 yellow pencils were removed from the box and the ratio of the number of grey pencils to the number of purple pencils to the number of yellow pencils became 2 : 3 : 7. Then some green pencils were added and the ratio of the number of yellow pencils to the number of green pencils was 7 : 4.

1. What was the ratio of the number of grey pencils to the number of purple pencils to the number of yellow pencils at first?
2. How many pencils were in the box in the end?

	Grey	Purple	Yellow	Green	Total
Before	2 u	3 u	7 u + 12	0	216
Change 1	No change	No change	- 12		- 12
After 1	2 u	3 u	7 u		204
Change 2	No change	No change	No change	+ 4 u
After 2	2 u	3 u	7 u	4 u

(a)
Total number of pencils at first
= 2 u + 3 u + 7 u + 12
= 12 u + 12

12 u + 12 = 216
12 u = 216 - 12
12 u = 204

1 u = 204 ÷ 12 = 17

Number of grey pencils at first
= 2 u
= 2 x 17
= 34

Number of purple pencils at first
= 3 u
= 3 x 17
= 51

Number of yellow pencils at first
= 7 u + 12
= 7 x 17 + 12
= 131 

At first
Grey pencils : Purple pencils : Yellow pencils
34 : 51 : 131

(b)
Total number of pencils in the box in the end
= 2 u + 3 u + 7 u + 4 u
= 16 u
= 272

Answer(s): (a) 34 : 51 : 131; (b) 272