The number of red files is thrice the number of brown files. The number of brown files is 5 more than the number of purple files. The total number of files is 135. The cost of each red file is $4.10 and the cost of each purple file is $1.70. The total cost of all the files is $461.90.

1. Find the number of purple files.
2. Find the cost of a brown file.

(a)
Number of purple files = 1 u
Number of brown files = 1 u + 5

Number of red files
= 3(1 u + 5)
= 3 u + 15

Total of number of files
= 1 u + 1 u + 5 + 3 u + 15
= 5 u + 20

5 u + 20 = 135
5 u = 135 - 20
5 u = 115

1 u = 115 ÷ 5 = 23

Number of purple files
= 1 u
= 23

(b)
Number of purple files = 23

Number of brown files
=  23 + 5
= 28

Number of red files
= 3 x 28
= 84

Cost of purple files 
= 23 x 1.70
= $39.10

Cost of red files 
= 84 x 4.10
= $344.40

Cost of brown files
= 461.90 - 344.40 - 39.10
= $78.40

Cost of 1 brown file
= 78.40 ÷ 28
= $2.80

Answer(s) (a) 23; (b) $2.80