Simon had an equal number of butter tarts, blueberry tarts and cream tarts. After he ate 30 butter tarts, some blueberry tarts and cream tarts, there were 38 tarts left. The number of blueberry tarts he ate was four times the number of cream tarts he ate. The number of blueberry tarts left was 14 more than the number of butter tarts left. How many butter tarts were there at first?

	Butter tarts	Blueberry tarts	Cream tarts	Total tarts
Before	1 p + 30	1 p + 4 u + 14	1 p + 4 u + 14
Change	- 30	- 4 u	- 1 u
After	1 p	1 p + 14	1 p + 14 + 1 u	38

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

1 p + 4 u + 14 = 1 p + 30
4 u = 30 - 14
4 u = 16

1 u = 16 ÷ 4 = 4

Total number of tarts in the end
= 1 p + 1 p + 14 + 1 p + 14 + 4
= 1 p + 1 p + 1 p + 14 + 14 + 4
= 3 p + 32

3 p + 32 = 38
3 p = 38 - 32
3 p = 6

1 p = 6 ÷ 3 = 2

Number of butter tarts at first
= 1 p + 30
= 2 + 30
= 32

Answer(s): 32