There were 177 purple, gold and green staplers in a box. 8 green staplers were removed from the box and the ratio of the number of purple staplers to the number of gold staplers to the number of green staplers became 2 : 4 : 7. Then some grey staplers were added and the ratio of the number of green staplers to the number of grey staplers was 7 : 4.

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

	Purple	Gold	Green	Grey	Total
Before	2 u	4 u	7 u + 8	0	177
Change 1	No change	No change	- 8		- 8
After 1	2 u	4 u	7 u		169
Change 2	No change	No change	No change	+ 4 u
After 2	2 u	4 u	7 u	4 u

(a)
Total number of staplers at first
= 2 u + 4 u + 7 u + 8
= 13 u + 8

13 u + 8 = 177
13 u = 177 - 8
13 u = 169

1 u = 169 ÷ 13 = 13

Number of purple staplers at first
= 2 u
= 2 x 13
= 26

Number of gold staplers at first
= 4 u
= 4 x 13
= 52

Number of green staplers at first
= 7 u + 8
= 7 x 13 + 8
= 99 

At first
Purple staplers : Gold staplers : Green staplers
26 : 52 : 99

(b)
Total number of staplers in the box in the end
= 2 u + 4 u + 7 u + 4 u
= 17 u
= 221

Answer(s): (a) 26 : 52 : 99; (b) 221