There were 259 grey, brown and purple pencils in a box. 7 purple pencils were removed from the box and the ratio of the number of grey pencils to the number of brown pencils to the number of purple pencils became 3 : 4 : 7. Then some green pencils were added and the ratio of the number of purple pencils to the number of green pencils was 7 : 5.

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

	Grey	Brown	Purple	Green	Total
Before	3 u	4 u	7 u + 7	0	259
Change 1	No change	No change	- 7		- 7
After 1	3 u	4 u	7 u		252
Change 2	No change	No change	No change	+ 5 u
After 2	3 u	4 u	7 u	5 u

(a)
Total number of pencils at first
= 3 u + 4 u + 7 u + 7
= 14 u + 7

14 u + 7 = 259
14 u = 259 - 7
14 u = 252

1 u = 252 ÷ 14 = 18

Number of grey pencils at first
= 3 u
= 3 x 18
= 54

Number of brown pencils at first
= 4 u
= 4 x 18
= 72

Number of purple pencils at first
= 7 u + 7
= 7 x 18 + 7
= 133 

At first
Grey pencils : Brown pencils : Purple pencils
54 : 72 : 133

(b)
Total number of pencils in the box in the end
= 3 u + 4 u + 7 u + 5 u
= 19 u
= 342

Answer(s): (a) 54 : 72 : 133; (b) 342