There were 231 white, gold and brown pencils in a box. 22 brown pencils were removed from the box and the ratio of the number of white pencils to the number of gold pencils to the number of brown pencils became 4 : 2 : 5. Then some silver pencils were added and the ratio of the number of brown pencils to the number of silver pencils was 5 : 5.

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

	White	Gold	Brown	Silver	Total
Before	4 u	2 u	5 u + 22	0	231
Change 1	No change	No change	- 22		- 22
After 1	4 u	2 u	5 u		209
Change 2	No change	No change	No change	+ 5 u
After 2	4 u	2 u	5 u	5 u

(a)
Total number of pencils at first
= 4 u + 2 u + 5 u + 22
= 11 u + 22

11 u + 22 = 231
11 u = 231 - 22
11 u = 209

1 u = 209 ÷ 11 = 19

Number of white pencils at first
= 4 u
= 4 x 19
= 76

Number of gold pencils at first
= 2 u
= 2 x 19
= 38

Number of brown pencils at first
= 5 u + 22
= 5 x 19 + 22
= 117 

At first
White pencils : Gold pencils : Brown pencils
76 : 38 : 117

(b)
Total number of pencils in the box in the end
= 4 u + 2 u + 5 u + 5 u
= 16 u
= 304

Answer(s): (a) 76 : 38 : 117; (b) 304