John had some banana muffins and vanilla muffins. ²₉ of the number of banana muffins was equal to ¹₃ of the number of vanilla muffins. After John made 144 more banana muffins, the number of banana muffins was ⁷₂ of the number of vanilla muffins. How many muffins did he have altogether in the end?
Make the numerators the same. LCM of 2 and 1 is 2.

29 of banana muffins = 1x23x2 of vanilla muffins

²₉ of banana muffins = ²₆ of vanilla muffins

	Banana muffins	Vanilla muffins	Total
Before	9 u	6 u
Change	+ 144
After	7x3 = 21 u	2x3 = 6 u	27 u

The number of vanilla muffins remains unchanged.  Make the number of vanilla muffins the same.  LCM of 2 and 6 is 6.

Number of more banana muffins made
= 21 u - 9 u
= 12 u

12 u = 144

1 u = 144 ÷ 12 = 12

Number of muffins that John had in the end
= 21 u + 6 u
= 27 u
= 27 x 12
= 324

Answer(s): 324