There were 241 white, green and gold pencils in a box. 13 gold pencils were removed from the box and the ratio of the number of white pencils to the number of green pencils to the number of gold pencils became 3 : 2 : 7. Then some black pencils were added and the ratio of the number of gold pencils to the number of black pencils was 7 : 6.

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

	White	Green	Gold	Black	Total
Before	3 u	2 u	7 u + 13	0	241
Change 1	No change	No change	- 13		- 13
After 1	3 u	2 u	7 u		228
Change 2	No change	No change	No change	+ 6 u
After 2	3 u	2 u	7 u	6 u

(a)
Total number of pencils at first
= 3 u + 2 u + 7 u + 13
= 12 u + 13

12 u + 13 = 241
12 u = 241 - 13
12 u = 228

1 u = 228 ÷ 12 = 19

Number of white pencils at first
= 3 u
= 3 x 19
= 57

Number of green pencils at first
= 2 u
= 2 x 19
= 38

Number of gold pencils at first
= 7 u + 13
= 7 x 19 + 13
= 146 

At first
White pencils : Green pencils : Gold pencils
57 : 38 : 146

(b)
Total number of pencils in the box in the end
= 3 u + 2 u + 7 u + 6 u
= 18 u
= 342

Answer(s): (a) 57 : 38 : 146; (b) 342