There were 199 yellow, purple and white staplers in a box. 19 white staplers were removed from the box and the ratio of the number of yellow staplers to the number of purple staplers to the number of white staplers became 3 : 4 : 5. Then some gold staplers were added and the ratio of the number of white staplers to the number of gold staplers was 5 : 7.

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

	Yellow	Purple	White	Gold	Total
Before	3 u	4 u	5 u + 19	0	199
Change 1	No change	No change	- 19		- 19
After 1	3 u	4 u	5 u		180
Change 2	No change	No change	No change	+ 7 u
After 2	3 u	4 u	5 u	7 u

(a)
Total number of staplers at first
= 3 u + 4 u + 5 u + 19
= 12 u + 19

12 u + 19 = 199
12 u = 199 - 19
12 u = 180

1 u = 180 ÷ 12 = 15

Number of yellow staplers at first
= 3 u
= 3 x 15
= 45

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

Number of white staplers at first
= 5 u + 19
= 5 x 15 + 19
= 94 

At first
Yellow staplers : Purple staplers : White staplers
45 : 60 : 94

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

Answer(s): (a) 45 : 60 : 94; (b) 285