Harry and Zane have some white files and some black files. The number of black files Harry has is equal to the number of white files Zane has. ¹₃ of Harry's files are white and ¹₄ of Zane's files are black. There are a total of 81 white files. Find the total number of files they have.

Harry		Zane		Total
White	Black	White	Black
	1x6	1x6
1x3	2x3	3x2	1x2
3 u	6 u	6 u	2 u	17 u

The number of Harry's black files and Zane's white files is the same.

The number of Harry's black files is repeated. The number of Zane's white files is repeated.  Make the number of Harry's black files and Zane's white files the same.  LCM of 2 and 3 is 6.

Number of white files
= 3 u + 6 u
= 9 u

9 u = 81

1 u = 81 ÷ 9 = 9

Total number of files
= 3 u + 6 u + 6 u + 2 u
= 17 u
= 17 x 9
= 153

Answer(s): 153