Michael and Ian have some black notebooks and some purple notebooks. The number of purple notebooks Michael has is equal to the number of black notebooks Ian has. ¹₃ of Michael's notebooks are black and ⁴₅ of Ian's notebooks are purple. There are a total of 12 black notebooks. Find the total number of notebooks they have.

Michael		Ian		Total
Black	Purple	Black	Purple
	1x2	1x2
1x1	2x1	1x2	4x2
1 u	2 u	2 u	8 u	13 u

The number of Michael's purple notebooks and Ian's black notebooks is the same.

The number of Michael's purple notebooks is repeated. The number of Ian's black notebooks is repeated.  Make the number of Michael's purple notebooks and Ian's black notebooks the same.  LCM of 2 and 3 is 2.

Number of black notebooks
= 1 u + 2 u
= 3 u

3 u = 12

1 u = 12 ÷ 3 = 4

Total number of notebooks
= 1 u + 2 u + 2 u + 8 u
= 13 u
= 13 x 4
= 52

Answer(s): 52