Peter had an equal number of butter muffins, vanila muffins and chocolate muffins. After he ate 39 butter muffins, some vanila muffins and chocolate muffins, there were 80 muffins left. The number of vanila muffins he ate was thrice the number of chocolate muffins he ate. The number of vanila muffins left was 24 more than the number of butter muffins left. How many butter muffins were there at first?

	Butter muffins	Vanila muffins	Chocolate muffins	Total muffins
Before	1 p + 39	1 p + 3 u + 24	1 p + 3 u + 24
Change	- 39	- 3 u	- 1 u
After	1 p	1 p + 24	1 p + 24 + 1 u	80

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

1 p + 3 u + 24 = 1 p + 39
3 u = 39 - 24
3 u = 15

1 u = 15 ÷ 3 = 5

Total number of muffins in the end
= 1 p + 1 p + 24 + 1 p + 24 + 5
= 1 p + 1 p + 1 p + 24 + 24 + 5
= 3 p + 53

3 p + 53 = 80
3 p = 80 - 53
3 p = 27

1 p = 27 ÷ 3 = 9

Number of butter muffins at first
= 1 p + 39
= 9 + 39
= 48

Answer(s): 48