There were 221 purple, green and blue pencils in a box. 11 blue pencils were removed from the box and the ratio of the number of purple pencils to the number of green pencils to the number of blue pencils became 5 : 2 : 7. Then some grey pencils were added and the ratio of the number of blue pencils to the number of grey pencils was 7 : 3.

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

	Purple	Green	Blue	Grey	Total
Before	5 u	2 u	7 u + 11	0	221
Change 1	No change	No change	- 11		- 11
After 1	5 u	2 u	7 u		210
Change 2	No change	No change	No change	+ 3 u
After 2	5 u	2 u	7 u	3 u

(a)
Total number of pencils at first
= 5 u + 2 u + 7 u + 11
= 14 u + 11

14 u + 11 = 221
14 u = 221 - 11
14 u = 210

1 u = 210 ÷ 14 = 15

Number of purple pencils at first
= 5 u
= 5 x 15
= 75

Number of green pencils at first
= 2 u
= 2 x 15
= 30

Number of blue pencils at first
= 7 u + 11
= 7 x 15 + 11
= 116 

At first
Purple pencils : Green pencils : Blue pencils
75 : 30 : 116

(b)
Total number of pencils in the box in the end
= 5 u + 2 u + 7 u + 3 u
= 17 u
= 255

Answer(s): (a) 75 : 30 : 116; (b) 255