Howard had an equal number of blueberry tarts, strawberry tarts and matcha tarts. After he ate 30 blueberry tarts, some strawberry tarts and matcha tarts, there were 54 tarts left. The number of strawberry tarts he ate was twice the number of matcha tarts he ate. The number of strawberry tarts left was 14 more than the number of blueberry tarts left. How many blueberry tarts were there at first?

	Blueberry tarts	Strawberry tarts	Matcha tarts	Total tarts
Before	1 p + 30	1 p + 2 u + 14	1 p + 2 u + 14
Change	- 30	- 2 u	- 1 u
After	1 p	1 p + 14	1 p + 14 + 1 u	54

Number of strawberry tarts and blueberry tarts was equal at first.

1 p + 2 u + 14 = 1 p + 30
2 u = 30 - 14
2 u = 16

1 u = 16 ÷ 2 = 8

Total number of tarts in the end
= 1 p + 1 p + 14 + 1 p + 14 + 8
= 1 p + 1 p + 1 p + 14 + 14 + 8
= 3 p + 36

3 p + 36 = 54
3 p = 54 - 36
3 p = 18

1 p = 18 ÷ 3 = 6

Number of blueberry tarts at first
= 1 p + 30
= 6 + 30
= 36

Answer(s): 36