There were 165 gold, blue and green notebooks in a box. 21 green notebooks were removed from the box and the ratio of the number of gold notebooks to the number of blue notebooks to the number of green notebooks became 4 : 2 : 3. Then some red notebooks were added and the ratio of the number of green notebooks to the number of red notebooks was 3 : 4.

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

	Gold	Blue	Green	Red	Total
Before	4 u	2 u	3 u + 21	0	165
Change 1	No change	No change	- 21		- 21
After 1	4 u	2 u	3 u		144
Change 2	No change	No change	No change	+ 4 u
After 2	4 u	2 u	3 u	4 u

(a)
Total number of notebooks at first
= 4 u + 2 u + 3 u + 21
= 9 u + 21

9 u + 21 = 165
9 u = 165 - 21
9 u = 144

1 u = 144 ÷ 9 = 16

Number of gold notebooks at first
= 4 u
= 4 x 16
= 64

Number of blue notebooks at first
= 2 u
= 2 x 16
= 32

Number of green notebooks at first
= 3 u + 21
= 3 x 16 + 21
= 69 

At first
Gold notebooks : Blue notebooks : Green notebooks
64 : 32 : 69

(b)
Total number of notebooks in the box in the end
= 4 u + 2 u + 3 u + 4 u
= 13 u
= 208

Answer(s): (a) 64 : 32 : 69; (b) 208