John had an equal number of vanila tarts, matcha tarts and blueberry tarts. After he ate 29 vanila tarts, some matcha tarts and blueberry tarts, there were 46 tarts left. The number of matcha tarts he ate was twice the number of blueberry tarts he ate. The number of matcha tarts left was 15 more than the number of vanila tarts left. How many vanila tarts were there at first?

	Vanila tarts	Matcha tarts	Blueberry tarts	Total tarts
Before	1 p + 29	1 p + 2 u + 15	1 p + 2 u + 15
Change	- 29	- 2 u	- 1 u
After	1 p	1 p + 15	1 p + 15 + 1 u	46

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

1 p + 2 u + 15 = 1 p + 29
2 u = 29 - 15
2 u = 14

1 u = 14 ÷ 2 = 7

Total number of tarts in the end
= 1 p + 1 p + 15 + 1 p + 15 + 7
= 1 p + 1 p + 1 p + 15 + 15 + 7
= 3 p + 37

3 p + 37 = 46
3 p = 46 - 37
3 p = 9

1 p = 9 ÷ 3 = 3

Number of vanila tarts at first
= 1 p + 29
= 3 + 29
= 32

Answer(s): 32