There were 111 white, purple and blue pens in a box. 13 blue pens were removed from the box and the ratio of the number of white pens to the number of purple pens to the number of blue pens became 5 : 2 : 7. Then some grey pens were added and the ratio of the number of blue pens to the number of grey pens was 7 : 5.

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

	White	Purple	Blue	Grey	Total
Before	5 u	2 u	7 u + 13	0	111
Change 1	No change	No change	- 13		- 13
After 1	5 u	2 u	7 u		98
Change 2	No change	No change	No change	+ 5 u
After 2	5 u	2 u	7 u	5 u

(a)
Total number of pens at first
= 5 u + 2 u + 7 u + 13
= 14 u + 13

14 u + 13 = 111
14 u = 111 - 13
14 u = 98

1 u = 98 ÷ 14 = 7

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

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

Number of blue pens at first
= 7 u + 13
= 7 x 7 + 13
= 62 

At first
White pens : Purple pens : Blue pens
35 : 14 : 62

(b)
Total number of pens in the box in the end
= 5 u + 2 u + 7 u + 5 u
= 19 u
= 133

Answer(s): (a) 35 : 14 : 62; (b) 133