The number of orange files is twice the number of purple files. The number of purple files is 5 more than the number of green files. The total number of files is 119. The cost of each orange file is $2.80 and the cost of each green file is $2.60. The total cost of all the files is $290.80.

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

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

Number of orange files
= 2(1 u + 5)
= 2 u + 10

Total of number of files
= 1 u + 1 u + 5 + 2 u + 10
= 4 u + 15

4 u + 15 = 119
4 u = 119 - 15
4 u = 104

1 u = 104 ÷ 4 = 26

Number of green files
= 1 u
= 26

(b)
Number of green files = 26

Number of purple files
=  26 + 5
= 31

Number of orange files
= 2 x 31
= 62

Cost of green files 
= 26 x 2.60
= $67.60

Cost of orange files 
= 62 x 2.80
= $173.60

Cost of purple files
= 290.80 - 173.60 - 67.60
= $49.60

Cost of 1 purple file
= 49.60 ÷ 31
= $1.60

Answer(s) (a) 26; (b) $1.60