Ethan and Jack have some purple notebooks and some grey notebooks. The number of grey notebooks Ethan has is equal to the number of purple notebooks Jack has. ¹₄ of Ethan's notebooks are purple and ²₃ of Jack's notebooks are grey. There are a total of 20 purple notebooks. Find the total number of notebooks they have.

Ethan		Jack		Total
Purple	Grey	Purple	Grey
	1x3	1x3
1x1	3x1	1x3	2x3
1 u	3 u	3 u	6 u	13 u

The number of Ethan's grey notebooks and Jack's purple notebooks is the same.

The number of Ethan's grey notebooks is repeated. The number of Jack's purple notebooks is repeated.  Make the number of Ethan's grey notebooks and Jack's purple notebooks the same.  LCM of 3 and 4 is 3.

Number of purple notebooks
= 1 u + 3 u
= 4 u

4 u = 20

1 u = 20 ÷ 4 = 5

Total number of notebooks
= 1 u + 3 u + 3 u + 6 u
= 13 u
= 13 x 5
= 65

Answer(s): 65