There were 263 green, blue and gold pens in a box. 11 gold pens were removed from the box and the ratio of the number of green pens to the number of blue pens to the number of gold pens became 5 : 4 : 9. Then some white pens were added and the ratio of the number of gold pens to the number of white pens was 9 : 2.

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

	Green	Blue	Gold	White	Total
Before	5 u	4 u	9 u + 11	0	263
Change 1	No change	No change	- 11		- 11
After 1	5 u	4 u	9 u		252
Change 2	No change	No change	No change	+ 2 u
After 2	5 u	4 u	9 u	2 u

(a)
Total number of pens at first
= 5 u + 4 u + 9 u + 11
= 18 u + 11

18 u + 11 = 263
18 u = 263 - 11
18 u = 252

1 u = 252 ÷ 18 = 14

Number of green pens at first
= 5 u
= 5 x 14
= 70

Number of blue pens at first
= 4 u
= 4 x 14
= 56

Number of gold pens at first
= 9 u + 11
= 9 x 14 + 11
= 137 

At first
Green pens : Blue pens : Gold pens
70 : 56 : 137

(b)
Total number of pens in the box in the end
= 5 u + 4 u + 9 u + 2 u
= 20 u
= 280

Answer(s): (a) 70 : 56 : 137; (b) 280