Pierre had an equal number of vanila muffins, matcha muffins and chocolate muffins. After he ate 45 vanila muffins, some matcha muffins and chocolate muffins, there were 44 muffins left. The number of matcha muffins he ate was thrice the number of chocolate muffins he ate. The number of matcha muffins left was 12 more than the number of vanila muffins left. How many vanila muffins were there at first?

	Vanila muffins	Matcha muffins	Chocolate muffins	Total muffins
Before	1 p + 45	1 p + 3 u + 12	1 p + 3 u + 12
Change	- 45	- 3 u	- 1 u
After	1 p	1 p + 12	1 p + 12 + 1 u	44

Number of matcha muffins and vanila muffins was equal at first.

1 p + 3 u + 12 = 1 p + 45
3 u = 45 - 12
3 u = 33

1 u = 33 ÷ 3 = 11

Total number of muffins in the end
= 1 p + 1 p + 12 + 1 p + 12 + 11
= 1 p + 1 p + 1 p + 12 + 12 + 11
= 3 p + 35

3 p + 35 = 44
3 p = 44 - 35
3 p = 9

1 p = 9 ÷ 3 = 3

Number of vanila muffins at first
= 1 p + 45
= 3 + 45
= 48

Answer(s): 48