Billy and Ryan have some brown pencils and some purple pencils. The number of purple pencils Billy has is equal to the number of brown pencils Ryan has. ¹₃ of Billy's pencils are brown and ⁴₅ of Ryan's pencils are purple. There are a total of 36 brown pencils. Find the total number of pencils they have.

Billy		Ryan		Total
Brown	Purple	Brown	Purple
	1x2	1x2
1x1	2x1	1x2	4x2
1 u	2 u	2 u	8 u	13 u

The number of Billy's purple pencils and Ryan's brown pencils is the same.

The number of Billy's purple pencils is repeated. The number of Ryan's brown pencils is repeated.  Make the number of Billy's purple pencils and Ryan's brown pencils the same.  LCM of 2 and 3 is 2.

Number of brown pencils
= 1 u + 2 u
= 3 u

3 u = 36

1 u = 36 ÷ 3 = 12

Total number of pencils
= 1 u + 2 u + 2 u + 8 u
= 13 u
= 13 x 12
= 156

Answer(s): 156