There were 302 brown, green and grey pencils in a box. 17 grey pencils were removed from the box and the ratio of the number of brown pencils to the number of green pencils to the number of grey pencils became 5 : 3 : 7. Then some yellow pencils were added and the ratio of the number of grey pencils to the number of yellow pencils was 7 : 3.

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

	Brown	Green	Grey	Yellow	Total
Before	5 u	3 u	7 u + 17	0	302
Change 1	No change	No change	- 17		- 17
After 1	5 u	3 u	7 u		285
Change 2	No change	No change	No change	+ 3 u
After 2	5 u	3 u	7 u	3 u

(a)
Total number of pencils at first
= 5 u + 3 u + 7 u + 17
= 15 u + 17

15 u + 17 = 302
15 u = 302 - 17
15 u = 285

1 u = 285 ÷ 15 = 19

Number of brown pencils at first
= 5 u
= 5 x 19
= 95

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

Number of grey pencils at first
= 7 u + 17
= 7 x 19 + 17
= 150 

At first
Brown pencils : Green pencils : Grey pencils
95 : 57 : 150

(b)
Total number of pencils in the box in the end
= 5 u + 3 u + 7 u + 3 u
= 18 u
= 342

Answer(s): (a) 95 : 57 : 150; (b) 342