Albert and Nick have some purple files and some green files. The number of green files Albert has is equal to the number of purple files Nick has. ²₃ of Albert's files are purple and ¹₆ of Nick's files are green. There are a total of 165 purple files. Find the total number of files they have.

Albert		Nick		Total
Purple	Green	Purple	Green
	1x5	1x5
2x5	1x5	5x1	1x1
10 u	5 u	5 u	1 u	21 u

The number of Albert's green files and Nick's purple files is the same.

The number of Albert's green files is repeated. The number of Nick's purple files is repeated.  Make the number of Albert's green files and Nick's purple files the same.  LCM of 1 and 3 is 5.

Number of purple files
= 10 u + 5 u
= 15 u

15 u = 165

1 u = 165 ÷ 15 = 11

Total number of files
= 10 u + 5 u + 5 u + 1 u
= 21 u
= 21 x 11
= 231

Answer(s): 231