There were 173 brown, gold and green pencils in a box. 8 green pencils were removed from the box and the ratio of the number of brown pencils to the number of gold pencils to the number of green pencils became 2 : 4 : 5. Then some purple pencils were added and the ratio of the number of green pencils to the number of purple pencils was 5 : 7.

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

	Brown	Gold	Green	Purple	Total
Before	2 u	4 u	5 u + 8	0	173
Change 1	No change	No change	- 8		- 8
After 1	2 u	4 u	5 u		165
Change 2	No change	No change	No change	+ 7 u
After 2	2 u	4 u	5 u	7 u

(a)
Total number of pencils at first
= 2 u + 4 u + 5 u + 8
= 11 u + 8

11 u + 8 = 173
11 u = 173 - 8
11 u = 165

1 u = 165 ÷ 11 = 15

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

Number of gold pencils at first
= 4 u
= 4 x 15
= 60

Number of green pencils at first
= 5 u + 8
= 5 x 15 + 8
= 83 

At first
Brown pencils : Gold pencils : Green pencils
30 : 60 : 83

(b)
Total number of pencils in the box in the end
= 2 u + 4 u + 5 u + 7 u
= 18 u
= 270

Answer(s): (a) 30 : 60 : 83; (b) 270