There were 137 yellow, white and gold pens in a box. 7 gold pens were removed from the box and the ratio of the number of yellow pens to the number of white pens to the number of gold pens became 3 : 2 : 5. Then some silver pens were added and the ratio of the number of gold pens to the number of silver pens was 5 : 7.

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

	Yellow	White	Gold	Silver	Total
Before	3 u	2 u	5 u + 7	0	137
Change 1	No change	No change	- 7		- 7
After 1	3 u	2 u	5 u		130
Change 2	No change	No change	No change	+ 7 u
After 2	3 u	2 u	5 u	7 u

(a)
Total number of pens at first
= 3 u + 2 u + 5 u + 7
= 10 u + 7

10 u + 7 = 137
10 u = 137 - 7
10 u = 130

1 u = 130 ÷ 10 = 13

Number of yellow pens at first
= 3 u
= 3 x 13
= 39

Number of white pens at first
= 2 u
= 2 x 13
= 26

Number of gold pens at first
= 5 u + 7
= 5 x 13 + 7
= 72 

At first
Yellow pens : White pens : Gold pens
39 : 26 : 72

(b)
Total number of pens in the box in the end
= 3 u + 2 u + 5 u + 7 u
= 17 u
= 221

Answer(s): (a) 39 : 26 : 72; (b) 221