The number of green files is thrice the number of yellow files. The number of yellow files is 10 more than the number of purple files. The total number of files is 105. The cost of each green file is $3.40 and the cost of each purple file is $2.90. The total cost of all the files is $309.10.

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

(a)
Number of purple files = 1 u
Number of yellow files = 1 u + 10

Number of green files
= 3(1 u + 10)
= 3 u + 30

Total of number of files
= 1 u + 1 u + 10 + 3 u + 30
= 5 u + 40

5 u + 40 = 105
5 u = 105 - 40
5 u = 65

1 u = 65 ÷ 5 = 13

Number of purple files
= 1 u
= 13

(b)
Number of purple files = 13

Number of yellow files
=  13 + 10
= 23

Number of green files
= 3 x 23
= 69

Cost of purple files 
= 13 x 2.90
= $37.70

Cost of green files 
= 69 x 3.40
= $234.60

Cost of yellow files
= 309.10 - 234.60 - 37.70
= $36.80

Cost of 1 yellow file
= 36.80 ÷ 23
= $1.60

Answer(s) (a) 13; (b) $1.60