The number of red files is thrice the number of orange files. The number of orange files is 8 more than the number of purple files. The total number of files is 137. The cost of each red file is $2.80 and the cost of each purple file is $2.10. The total cost of all the files is $322.50.
- Find the number of purple files.
- Find the cost of a orange file.
(a)
Number of purple files = 1 u
Number of orange files = 1 u + 8
Number of red files
= 3(1 u + 8)
= 3 u + 24
Total of number of files
= 1 u + 1 u + 8 + 3 u + 24
= 5 u + 32
5 u + 32 = 137
5 u = 137 - 32
5 u = 105
1 u = 105 ÷ 5 = 21
Number of purple files
= 1 u
= 21
(b)
Number of purple files = 21
Number of orange files
= 21 + 8
= 29
Number of red files
= 3 x 29
= 87
Cost of purple files
= 21 x 2.10
= $44.10
Cost of red files
= 87 x 2.80
= $243.60
Cost of orange files
= 322.50 - 243.60 - 44.10
= $34.80
Cost of 1 orange file
= 34.80 ÷ 29
= $1.20
Answer(s) (a) 21; (b) $1.20
