The number of red files is twice the number of yellow files. The number of yellow files is 5 more than the number of orange files. The total number of files is 123. The cost of each red file is $2.80 and the cost of each orange file is $2.30. The total cost of all the files is $286.10.
- Find the number of orange files.
- Find the cost of a yellow file.
(a)
Number of orange files = 1 u
Number of yellow files = 1 u + 5
Number of red 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 = 123
4 u = 123 - 15
4 u = 108
1 u = 108 ÷ 4 = 27
Number of orange files
= 1 u
= 27
(b)
Number of orange files = 27
Number of yellow files
= 27 + 5
= 32
Number of red files
= 2 x 32
= 64
Cost of orange files
= 27 x 2.30
= $62.10
Cost of red files
= 64 x 2.80
= $179.20
Cost of yellow files
= 286.10 - 179.20 - 62.10
= $44.80
Cost of 1 yellow file
= 44.80 ÷ 32
= $1.40
Answer(s) (a) 27; (b) $1.40
