There were 88 gold, green and black pens in a box. 4 black pens were removed from the box and the ratio of the number of gold pens to the number of green pens to the number of black pens became 3 : 2 : 7. Then some pink pens were added and the ratio of the number of black pens to the number of pink pens was 7 : 7.

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

	Gold	Green	Black	Pink	Total
Before	3 u	2 u	7 u + 4	0	88
Change 1	No change	No change	- 4		- 4
After 1	3 u	2 u	7 u		84
Change 2	No change	No change	No change	+ 7 u
After 2	3 u	2 u	7 u	7 u

(a)
Total number of pens at first
= 3 u + 2 u + 7 u + 4
= 12 u + 4

12 u + 4 = 88
12 u = 88 - 4
12 u = 84

1 u = 84 ÷ 12 = 7

Number of gold pens at first
= 3 u
= 3 x 7
= 21

Number of green pens at first
= 2 u
= 2 x 7
= 14

Number of black pens at first
= 7 u + 4
= 7 x 7 + 4
= 53 

At first
Gold pens : Green pens : Black pens
21 : 14 : 53

(b)
Total number of pens in the box in the end
= 3 u + 2 u + 7 u + 7 u
= 19 u
= 133

Answer(s): (a) 21 : 14 : 53; (b) 133