David had some vanilla muffins and apple muffins. ⁴₇ of the number of vanilla muffins was equal to ¹₅ of the number of apple muffins. After David made 16 more vanilla muffins, the number of vanilla muffins was ³₄ of the number of apple muffins. How many muffins did he have altogether in the end?
Make the numerators the same. LCM of 4 and 1 is 4.

47 of vanilla muffins = 1x45x4 of apple muffins

⁴₇ of vanilla muffins = ⁴₂₀ of apple muffins

	Vanilla muffins	Apple muffins	Total
Before	7 u	20 u
Change	+ 16
After	3x5 = 15 u	4x5 = 20 u	35 u

The number of apple muffins remains unchanged.  Make the number of apple muffins the same.  LCM of 4 and 20 is 20.

Number of more vanilla muffins made
= 15 u - 7 u
= 8 u

8 u = 16

1 u = 16 ÷ 8 = 2

Number of muffins that David had in the end
= 15 u + 20 u
= 35 u
= 35 x 2
= 70

Answer(s): 70