There were 181 white, silver and purple pencils in a box. 10 purple pencils were removed from the box and the ratio of the number of white pencils to the number of silver pencils to the number of purple pencils became 2 : 4 : 3. Then some gold pencils were added and the ratio of the number of purple pencils to the number of gold pencils was 3 : 3.

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

	White	Silver	Purple	Gold	Total
Before	2 u	4 u	3 u + 10	0	181
Change 1	No change	No change	- 10		- 10
After 1	2 u	4 u	3 u		171
Change 2	No change	No change	No change	+ 3 u
After 2	2 u	4 u	3 u	3 u

(a)
Total number of pencils at first
= 2 u + 4 u + 3 u + 10
= 9 u + 10

9 u + 10 = 181
9 u = 181 - 10
9 u = 171

1 u = 171 ÷ 9 = 19

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

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

Number of purple pencils at first
= 3 u + 10
= 3 x 19 + 10
= 67 

At first
White pencils : Silver pencils : Purple pencils
38 : 76 : 67

(b)
Total number of pencils in the box in the end
= 2 u + 4 u + 3 u + 3 u
= 12 u
= 228

Answer(s): (a) 38 : 76 : 67; (b) 228