There were 141 blue, red and gold pencils in a box. 15 gold pencils were removed from the box and the ratio of the number of blue pencils to the number of red pencils to the number of gold pencils became 2 : 4 : 3. Then some yellow pencils were added and the ratio of the number of gold pencils to the number of yellow pencils was 3 : 6.

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

	Blue	Red	Gold	Yellow	Total
Before	2 u	4 u	3 u + 15	0	141
Change 1	No change	No change	- 15		- 15
After 1	2 u	4 u	3 u		126
Change 2	No change	No change	No change	+ 6 u
After 2	2 u	4 u	3 u	6 u

(a)
Total number of pencils at first
= 2 u + 4 u + 3 u + 15
= 9 u + 15

9 u + 15 = 141
9 u = 141 - 15
9 u = 126

1 u = 126 ÷ 9 = 14

Number of blue pencils at first
= 2 u
= 2 x 14
= 28

Number of red pencils at first
= 4 u
= 4 x 14
= 56

Number of gold pencils at first
= 3 u + 15
= 3 x 14 + 15
= 57 

At first
Blue pencils : Red pencils : Gold pencils
28 : 56 : 57

(b)
Total number of pencils in the box in the end
= 2 u + 4 u + 3 u + 6 u
= 15 u
= 210

Answer(s): (a) 28 : 56 : 57; (b) 210