Liam had an equal number of vanila doughnuts, blueberry doughnuts and chocolate doughnuts. After he ate 19 vanila doughnuts, some blueberry doughnuts and chocolate doughnuts, there were 65 doughnuts left. The number of blueberry doughnuts he ate was twice the number of chocolate doughnuts he ate. The number of blueberry doughnuts left was 13 more than the number of vanila doughnuts left. How many vanila doughnuts were there at first?

	Vanila doughnuts	Blueberry doughnuts	Chocolate doughnuts	Total doughnuts
Before	1 p + 19	1 p + 2 u + 13	1 p + 2 u + 13
Change	- 19	- 2 u	- 1 u
After	1 p	1 p + 13	1 p + 13 + 1 u	65

Number of blueberry doughnuts and vanila doughnuts was equal at first.

1 p + 2 u + 13 = 1 p + 19
2 u = 19 - 13
2 u = 6

1 u = 6 ÷ 2 = 3

Total number of doughnuts in the end
= 1 p + 1 p + 13 + 1 p + 13 + 3
= 1 p + 1 p + 1 p + 13 + 13 + 3
= 3 p + 29

3 p + 29 = 65
3 p = 65 - 29
3 p = 36

1 p = 36 ÷ 3 = 12

Number of vanila doughnuts at first
= 1 p + 19
= 12 + 19
= 31

Answer(s): 31