There were 175 pink, brown and gold pencils in a box. 19 gold pencils were removed from the box and the ratio of the number of pink pencils to the number of brown pencils to the number of gold pencils became 3 : 4 : 5. Then some black pencils were added and the ratio of the number of gold pencils to the number of black pencils was 5 : 3.

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

	Pink	Brown	Gold	Black	Total
Before	3 u	4 u	5 u + 19	0	175
Change 1	No change	No change	- 19		- 19
After 1	3 u	4 u	5 u		156
Change 2	No change	No change	No change	+ 3 u
After 2	3 u	4 u	5 u	3 u

(a)
Total number of pencils at first
= 3 u + 4 u + 5 u + 19
= 12 u + 19

12 u + 19 = 175
12 u = 175 - 19
12 u = 156

1 u = 156 ÷ 12 = 13

Number of pink pencils at first
= 3 u
= 3 x 13
= 39

Number of brown pencils at first
= 4 u
= 4 x 13
= 52

Number of gold pencils at first
= 5 u + 19
= 5 x 13 + 19
= 84 

At first
Pink pencils : Brown pencils : Gold pencils
39 : 52 : 84

(b)
Total number of pencils in the box in the end
= 3 u + 4 u + 5 u + 3 u
= 15 u
= 195

Answer(s): (a) 39 : 52 : 84; (b) 195