There were 269 silver, red and white pencils in a box. 14 white pencils were removed from the box and the ratio of the number of silver pencils to the number of red pencils to the number of white pencils became 3 : 5 : 7. Then some gold pencils were added and the ratio of the number of white pencils to the number of gold pencils was 7 : 2.

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

	Silver	Red	White	Gold	Total
Before	3 u	5 u	7 u + 14	0	269
Change 1	No change	No change	- 14		- 14
After 1	3 u	5 u	7 u		255
Change 2	No change	No change	No change	+ 2 u
After 2	3 u	5 u	7 u	2 u

(a)
Total number of pencils at first
= 3 u + 5 u + 7 u + 14
= 15 u + 14

15 u + 14 = 269
15 u = 269 - 14
15 u = 255

1 u = 255 ÷ 15 = 17

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

Number of red pencils at first
= 5 u
= 5 x 17
= 85

Number of white pencils at first
= 7 u + 14
= 7 x 17 + 14
= 133 

At first
Silver pencils : Red pencils : White pencils
51 : 85 : 133

(b)
Total number of pencils in the box in the end
= 3 u + 5 u + 7 u + 2 u
= 17 u
= 289

Answer(s): (a) 51 : 85 : 133; (b) 289