There were 156 black, green and brown pens in a box. 24 brown pens were removed from the box and the ratio of the number of black pens to the number of green pens to the number of brown pens became 4 : 3 : 5. Then some grey pens were added and the ratio of the number of brown pens to the number of grey pens was 5 : 4.

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

	Black	Green	Brown	Grey	Total
Before	4 u	3 u	5 u + 24	0	156
Change 1	No change	No change	- 24		- 24
After 1	4 u	3 u	5 u		132
Change 2	No change	No change	No change	+ 4 u
After 2	4 u	3 u	5 u	4 u

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

12 u + 24 = 156
12 u = 156 - 24
12 u = 132

1 u = 132 ÷ 12 = 11

Number of black pens at first
= 4 u
= 4 x 11
= 44

Number of green pens at first
= 3 u
= 3 x 11
= 33

Number of brown pens at first
= 5 u + 24
= 5 x 11 + 24
= 79 

At first
Black pens : Green pens : Brown pens
44 : 33 : 79

(b)
Total number of pens in the box in the end
= 4 u + 3 u + 5 u + 4 u
= 16 u
= 176

Answer(s): (a) 44 : 33 : 79; (b) 176