There were 61 silver, green and grey pencils in a box. 11 grey pencils were removed from the box and the ratio of the number of silver pencils to the number of green pencils to the number of grey pencils became 2 : 5 : 3. Then some black pencils were added and the ratio of the number of grey pencils to the number of black pencils was 3 : 3.

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

	Silver	Green	Grey	Black	Total
Before	2 u	5 u	3 u + 11	0	61
Change 1	No change	No change	- 11		- 11
After 1	2 u	5 u	3 u		50
Change 2	No change	No change	No change	+ 3 u
After 2	2 u	5 u	3 u	3 u

(a)
Total number of pencils at first
= 2 u + 5 u + 3 u + 11
= 10 u + 11

10 u + 11 = 61
10 u = 61 - 11
10 u = 50

1 u = 50 ÷ 10 = 5

Number of silver pencils at first
= 2 u
= 2 x 5
= 10

Number of green pencils at first
= 5 u
= 5 x 5
= 25

Number of grey pencils at first
= 3 u + 11
= 3 x 5 + 11
= 26 

At first
Silver pencils : Green pencils : Grey pencils
10 : 25 : 26

(b)
Total number of pencils in the box in the end
= 2 u + 5 u + 3 u + 3 u
= 13 u
= 65

Answer(s): (a) 10 : 25 : 26; (b) 65