There were 194 green, grey and purple staplers in a box. 14 purple staplers were removed from the box and the ratio of the number of green staplers to the number of grey staplers to the number of purple staplers became 4 : 5 : 3. Then some red staplers were added and the ratio of the number of purple staplers to the number of red staplers was 3 : 7.

1. What was the ratio of the number of green staplers to the number of grey staplers to the number of purple staplers at first?
2. How many staplers were in the box in the end?

	Green	Grey	Purple	Red	Total
Before	4 u	5 u	3 u + 14	0	194
Change 1	No change	No change	- 14		- 14
After 1	4 u	5 u	3 u		180
Change 2	No change	No change	No change	+ 7 u
After 2	4 u	5 u	3 u	7 u

(a)
Total number of staplers at first
= 4 u + 5 u + 3 u + 14
= 12 u + 14

12 u + 14 = 194
12 u = 194 - 14
12 u = 180

1 u = 180 ÷ 12 = 15

Number of green staplers at first
= 4 u
= 4 x 15
= 60

Number of grey staplers at first
= 5 u
= 5 x 15
= 75

Number of purple staplers at first
= 3 u + 14
= 3 x 15 + 14
= 59 

At first
Green staplers : Grey staplers : Purple staplers
60 : 75 : 59

(b)
Total number of staplers in the box in the end
= 4 u + 5 u + 3 u + 7 u
= 19 u
= 285

Answer(s): (a) 60 : 75 : 59; (b) 285