There were 112 grey, purple and yellow pencils in a box. 2 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 5 : 2 : 3. Then some silver pencils were added and the ratio of the number of yellow pencils to the number of silver pencils was 3 : 8.

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	Silver	Total
Before	5 u	2 u	3 u + 2	0	112
Change 1	No change	No change	- 2		- 2
After 1	5 u	2 u	3 u		110
Change 2	No change	No change	No change	+ 8 u
After 2	5 u	2 u	3 u	8 u

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

10 u + 2 = 112
10 u = 112 - 2
10 u = 110

1 u = 110 ÷ 10 = 11

Number of grey pencils at first
= 5 u
= 5 x 11
= 55

Number of purple pencils at first
= 2 u
= 2 x 11
= 22

Number of yellow pencils at first
= 3 u + 2
= 3 x 11 + 2
= 35 

At first
Grey pencils : Purple pencils : Yellow pencils
55 : 22 : 35

(b)
Total number of pencils in the box in the end
= 5 u + 2 u + 3 u + 8 u
= 18 u
= 198

Answer(s): (a) 55 : 22 : 35; (b) 198