Oliver had an equal number of vanila tarts, butter tarts and cream tarts. After he ate 28 vanila tarts, some butter tarts and cream tarts, there were 47 tarts left. The number of butter tarts he ate was twice the number of cream tarts he ate. The number of butter tarts left was 16 more than the number of vanila tarts left. How many vanila tarts were there at first?

	Vanila tarts	Butter tarts	Cream tarts	Total tarts
Before	1 p + 28	1 p + 2 u + 16	1 p + 2 u + 16
Change	- 28	- 2 u	- 1 u
After	1 p	1 p + 16	1 p + 16 + 1 u	47

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

1 p + 2 u + 16 = 1 p + 28
2 u = 28 - 16
2 u = 12

1 u = 12 ÷ 2 = 6

Total number of tarts in the end
= 1 p + 1 p + 16 + 1 p + 16 + 6
= 1 p + 1 p + 1 p + 16 + 16 + 6
= 3 p + 38

3 p + 38 = 47
3 p = 47 - 38
3 p = 9

1 p = 9 ÷ 3 = 3

Number of vanila tarts at first
= 1 p + 28
= 3 + 28
= 31

Answer(s): 31