Mark had an equal number of matcha doughnuts, butter doughnuts and chocolate doughnuts. After he ate 34 matcha doughnuts, some butter doughnuts and chocolate doughnuts, there were 49 doughnuts left. The number of butter doughnuts he ate was four times the number of chocolate doughnuts he ate. The number of butter doughnuts left was 18 more than the number of matcha doughnuts left. How many matcha doughnuts were there at first?

	Matcha doughnuts	Butter doughnuts	Chocolate doughnuts	Total doughnuts
Before	1 p + 34	1 p + 4 u + 18	1 p + 4 u + 18
Change	- 34	- 4 u	- 1 u
After	1 p	1 p + 18	1 p + 18 + 1 u	49

Number of butter doughnuts and matcha doughnuts was equal at first.

1 p + 4 u + 18 = 1 p + 34
4 u = 34 - 18
4 u = 16

1 u = 16 ÷ 4 = 4

Total number of doughnuts in the end
= 1 p + 1 p + 18 + 1 p + 18 + 4
= 1 p + 1 p + 1 p + 18 + 18 + 4
= 3 p + 40

3 p + 40 = 49
3 p = 49 - 40
3 p = 9

1 p = 9 ÷ 3 = 3

Number of matcha doughnuts at first
= 1 p + 34
= 3 + 34
= 37

Answer(s): 37