There were 221 green, brown and gold pencils in a box. 5 gold pencils were removed from the box and the ratio of the number of green pencils to the number of brown pencils to the number of gold pencils became 5 : 4 : 9. Then some blue pencils were added and the ratio of the number of gold pencils to the number of blue pencils was 9 : 3.

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

	Green	Brown	Gold	Blue	Total
Before	5 u	4 u	9 u + 5	0	221
Change 1	No change	No change	- 5		- 5
After 1	5 u	4 u	9 u		216
Change 2	No change	No change	No change	+ 3 u
After 2	5 u	4 u	9 u	3 u

(a)
Total number of pencils at first
= 5 u + 4 u + 9 u + 5
= 18 u + 5

18 u + 5 = 221
18 u = 221 - 5
18 u = 216

1 u = 216 ÷ 18 = 12

Number of green pencils at first
= 5 u
= 5 x 12
= 60

Number of brown pencils at first
= 4 u
= 4 x 12
= 48

Number of gold pencils at first
= 9 u + 5
= 9 x 12 + 5
= 113 

At first
Green pencils : Brown pencils : Gold pencils
60 : 48 : 113

(b)
Total number of pencils in the box in the end
= 5 u + 4 u + 9 u + 3 u
= 21 u
= 252

Answer(s): (a) 60 : 48 : 113; (b) 252