There were 212 red, yellow and pink pencils in a box. 8 pink pencils were removed from the box and the ratio of the number of red pencils to the number of yellow pencils to the number of pink pencils became 3 : 2 : 7. Then some black pencils were added and the ratio of the number of pink pencils to the number of black pencils was 7 : 6.

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

	Red	Yellow	Pink	Black	Total
Before	3 u	2 u	7 u + 8	0	212
Change 1	No change	No change	- 8		- 8
After 1	3 u	2 u	7 u		204
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 + 8
= 12 u + 8

12 u + 8 = 212
12 u = 212 - 8
12 u = 204

1 u = 204 ÷ 12 = 17

Number of red pencils at first
= 3 u
= 3 x 17
= 51

Number of yellow pencils at first
= 2 u
= 2 x 17
= 34

Number of pink pencils at first
= 7 u + 8
= 7 x 17 + 8
= 127 

At first
Red pencils : Yellow pencils : Pink pencils
51 : 34 : 127

(b)
Total number of pencils in the box in the end
= 3 u + 2 u + 7 u + 6 u
= 18 u
= 306

Answer(s): (a) 51 : 34 : 127; (b) 306