There were 228 green, brown and black pencils in a box. 24 black 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 black pencils became 4 : 3 : 5. Then some gold pencils were added and the ratio of the number of black pencils to the number of gold pencils was 5 : 4.

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

	Green	Brown	Black	Gold	Total
Before	4 u	3 u	5 u + 24	0	228
Change 1	No change	No change	- 24		- 24
After 1	4 u	3 u	5 u		204
Change 2	No change	No change	No change	+ 4 u
After 2	4 u	3 u	5 u	4 u

(a)
Total number of pencils at first
= 4 u + 3 u + 5 u + 24
= 12 u + 24

12 u + 24 = 228
12 u = 228 - 24
12 u = 204

1 u = 204 ÷ 12 = 17

Number of green pencils at first
= 4 u
= 4 x 17
= 68

Number of brown pencils at first
= 3 u
= 3 x 17
= 51

Number of black pencils at first
= 5 u + 24
= 5 x 17 + 24
= 109 

At first
Green pencils : Brown pencils : Black pencils
68 : 51 : 109

(b)
Total number of pencils in the box in the end
= 4 u + 3 u + 5 u + 4 u
= 16 u
= 272

Answer(s): (a) 68 : 51 : 109; (b) 272