There were 301 blue, pink and purple pencils in a box. 16 purple pencils were removed from the box and the ratio of the number of blue pencils to the number of pink pencils to the number of purple pencils became 4 : 2 : 9. Then some yellow pencils were added and the ratio of the number of purple pencils to the number of yellow pencils was 9 : 7.

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

	Blue	Pink	Purple	Yellow	Total
Before	4 u	2 u	9 u + 16	0	301
Change 1	No change	No change	- 16		- 16
After 1	4 u	2 u	9 u		285
Change 2	No change	No change	No change	+ 7 u
After 2	4 u	2 u	9 u	7 u

(a)
Total number of pencils at first
= 4 u + 2 u + 9 u + 16
= 15 u + 16

15 u + 16 = 301
15 u = 301 - 16
15 u = 285

1 u = 285 ÷ 15 = 19

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

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

Number of purple pencils at first
= 9 u + 16
= 9 x 19 + 16
= 187 

At first
Blue pencils : Pink pencils : Purple pencils
76 : 38 : 187

(b)
Total number of pencils in the box in the end
= 4 u + 2 u + 9 u + 7 u
= 22 u
= 418

Answer(s): (a) 76 : 38 : 187; (b) 418