There were 175 yellow, red and gold pencils in a box. 19 gold pencils were removed from the box and the ratio of the number of yellow pencils to the number of red pencils to the number of gold pencils became 3 : 4 : 5. Then some green pencils were added and the ratio of the number of gold pencils to the number of green pencils was 5 : 2.

1. What was the ratio of the number of yellow 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?

	Yellow	Red	Gold	Green	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	+ 2 u
After 2	3 u	4 u	5 u	2 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 yellow pencils at first
= 3 u
= 3 x 13
= 39

Number of red 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
Yellow pencils : Red pencils : Gold pencils
39 : 52 : 84

(b)
Total number of pencils in the box in the end
= 3 u + 4 u + 5 u + 2 u
= 14 u
= 182

Answer(s): (a) 39 : 52 : 84; (b) 182