There were 159 yellow, blue and purple pens in a box. 5 purple pens were removed from the box and the ratio of the number of yellow pens to the number of blue pens to the number of purple pens became 2 : 5 : 7. Then some silver pens were added and the ratio of the number of purple pens to the number of silver pens was 7 : 3.

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

	Yellow	Blue	Purple	Silver	Total
Before	2 u	5 u	7 u + 5	0	159
Change 1	No change	No change	- 5		- 5
After 1	2 u	5 u	7 u		154
Change 2	No change	No change	No change	+ 3 u
After 2	2 u	5 u	7 u	3 u

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

14 u + 5 = 159
14 u = 159 - 5
14 u = 154

1 u = 154 ÷ 14 = 11

Number of yellow pens at first
= 2 u
= 2 x 11
= 22

Number of blue pens at first
= 5 u
= 5 x 11
= 55

Number of purple pens at first
= 7 u + 5
= 7 x 11 + 5
= 82 

At first
Yellow pens : Blue pens : Purple pens
22 : 55 : 82

(b)
Total number of pens in the box in the end
= 2 u + 5 u + 7 u + 3 u
= 17 u
= 187

Answer(s): (a) 22 : 55 : 82; (b) 187