The number of brown files is twice the number of green files. The number of green files is 5 more than the number of purple files. The total number of files is 111. The cost of each brown file is $3.60 and the cost of each purple file is $2.90. The total cost of all the files is $321.90.
- Find the number of purple files.
- Find the cost of a green file.
(a)
Number of purple files = 1 u
Number of green files = 1 u + 5
Number of brown 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 = 111
4 u = 111 - 15
4 u = 96
1 u = 96 ÷ 4 = 24
Number of purple files
= 1 u
= 24
(b)
Number of purple files = 24
Number of green files
= 24 + 5
= 29
Number of brown files
= 2 x 29
= 58
Cost of purple files
= 24 x 2.90
= $69.60
Cost of brown files
= 58 x 3.60
= $208.80
Cost of green files
= 321.90 - 208.80 - 69.60
= $43.50
Cost of 1 green file
= 43.50 ÷ 29
= $1.50
Answer(s) (a) 24; (b) $1.50