The number of purple files is twice the number of orange files. The number of orange files is 10 more than the number of blue files. The total number of files is 134. The cost of each purple file is $4.30 and the cost of each blue file is $2.60. The total cost of all the files is $445.60.

1. Find the number of blue files.
2. Find the cost of a orange file.

(a)
Number of blue files = 1 u
Number of orange files = 1 u + 10

Number of purple files
= 2(1 u + 10)
= 2 u + 20

Total of number of files
= 1 u + 1 u + 10 + 2 u + 20
= 4 u + 30

4 u + 30 = 134
4 u = 134 - 30
4 u = 104

1 u = 104 ÷ 4 = 26

Number of blue files
= 1 u
= 26

(b)
Number of blue files = 26

Number of orange files
=  26 + 10
= 36

Number of purple files
= 2 x 36
= 72

Cost of blue files 
= 26 x 2.60
= $67.60

Cost of purple files 
= 72 x 4.30
= $309.60

Cost of orange files
= 445.60 - 309.60 - 67.60
= $68.40

Cost of 1 orange file
= 68.40 ÷ 36
= $1.90

Answer(s) (a) 26; (b) $1.90