There were 151 purple, yellow and brown files in a box. 19 brown files were removed from the box and the ratio of the number of purple files to the number of yellow files to the number of brown files became 3 : 4 : 5. Then some white files were added and the ratio of the number of brown files to the number of white files was 5 : 8.

1. What was the ratio of the number of purple files to the number of yellow files to the number of brown files at first?
2. How many files were in the box in the end?

	Purple	Yellow	Brown	White	Total
Before	3 u	4 u	5 u + 19	0	151
Change 1	No change	No change	- 19		- 19
After 1	3 u	4 u	5 u		132
Change 2	No change	No change	No change	+ 8 u
After 2	3 u	4 u	5 u	8 u

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

12 u + 19 = 151
12 u = 151 - 19
12 u = 132

1 u = 132 ÷ 12 = 11

Number of purple files at first
= 3 u
= 3 x 11
= 33

Number of yellow files at first
= 4 u
= 4 x 11
= 44

Number of brown files at first
= 5 u + 19
= 5 x 11 + 19
= 74 

At first
Purple files : Yellow files : Brown files
33 : 44 : 74

(b)
Total number of files in the box in the end
= 3 u + 4 u + 5 u + 8 u
= 20 u
= 220

Answer(s): (a) 33 : 44 : 74; (b) 220