There were 121 grey, pink and red pencils in a box. 25 red pencils were removed from the box and the ratio of the number of grey pencils to the number of pink pencils to the number of red pencils became 3 : 2 : 7. Then some green pencils were added and the ratio of the number of red pencils to the number of green pencils was 7 : 3.

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

	Grey	Pink	Red	Green	Total
Before	3 u	2 u	7 u + 25	0	121
Change 1	No change	No change	- 25		- 25
After 1	3 u	2 u	7 u		96
Change 2	No change	No change	No change	+ 3 u
After 2	3 u	2 u	7 u	3 u

(a)
Total number of pencils at first
= 3 u + 2 u + 7 u + 25
= 12 u + 25

12 u + 25 = 121
12 u = 121 - 25
12 u = 96

1 u = 96 ÷ 12 = 8

Number of grey pencils at first
= 3 u
= 3 x 8
= 24

Number of pink pencils at first
= 2 u
= 2 x 8
= 16

Number of red pencils at first
= 7 u + 25
= 7 x 8 + 25
= 81 

At first
Grey pencils : Pink pencils : Red pencils
24 : 16 : 81

(b)
Total number of pencils in the box in the end
= 3 u + 2 u + 7 u + 3 u
= 15 u
= 120

Answer(s): (a) 24 : 16 : 81; (b) 120