There were 100 white, yellow and purple notebooks in a box. 16 purple notebooks were removed from the box and the ratio of the number of white notebooks to the number of yellow notebooks to the number of purple notebooks became 5 : 4 : 3. Then some green notebooks were added and the ratio of the number of purple notebooks to the number of green notebooks was 3 : 2.

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

	White	Yellow	Purple	Green	Total
Before	5 u	4 u	3 u + 16	0	100
Change 1	No change	No change	- 16		- 16
After 1	5 u	4 u	3 u		84
Change 2	No change	No change	No change	+ 2 u
After 2	5 u	4 u	3 u	2 u

(a)
Total number of notebooks at first
= 5 u + 4 u + 3 u + 16
= 12 u + 16

12 u + 16 = 100
12 u = 100 - 16
12 u = 84

1 u = 84 ÷ 12 = 7

Number of white notebooks at first
= 5 u
= 5 x 7
= 35

Number of yellow notebooks at first
= 4 u
= 4 x 7
= 28

Number of purple notebooks at first
= 3 u + 16
= 3 x 7 + 16
= 37 

At first
White notebooks : Yellow notebooks : Purple notebooks
35 : 28 : 37

(b)
Total number of notebooks in the box in the end
= 5 u + 4 u + 3 u + 2 u
= 14 u
= 98

Answer(s): (a) 35 : 28 : 37; (b) 98