Seth had some vanilla muffins and banana muffins. ²₅ of the number of vanilla muffins was equal to ¹₅ of the number of banana muffins. After Seth made 30 more vanilla muffins, the number of vanilla muffins was ³₂ of the number of banana muffins. How many muffins did he have altogether in the end?
Make the numerators the same. LCM of 2 and 1 is 2.

25 of vanilla muffins = 1x25x2 of banana muffins

²₅ of vanilla muffins = ²₁₀ of banana muffins

	Vanilla muffins	Banana muffins	Total
Before	5 u	10 u
Change	+ 30
After	3x5 = 15 u	2x5 = 10 u	25 u

The number of banana muffins remains unchanged.  Make the number of banana muffins the same.  LCM of 2 and 10 is 10.

Number of more vanilla muffins made
= 15 u - 5 u
= 10 u

10 u = 30

1 u = 30 ÷ 10 = 3

Number of muffins that Seth had in the end
= 15 u + 10 u
= 25 u
= 25 x 3
= 75

Answer(s): 75