Ian had an equal number of vanila cupcakes, chocolate cupcakes and blueberry cupcakes. After he ate 36 vanila cupcakes, some chocolate cupcakes and blueberry cupcakes, there were 73 cupcakes left. The number of chocolate cupcakes he ate was thrice the number of blueberry cupcakes he ate. The number of chocolate cupcakes left was 15 more than the number of vanila cupcakes left. How many vanila cupcakes were there at first?

	Vanila cupcakes	Chocolate cupcakes	Blueberry cupcakes	Total cupcakes
Before	1 p + 36	1 p + 3 u + 15	1 p + 3 u + 15
Change	- 36	- 3 u	- 1 u
After	1 p	1 p + 15	1 p + 15 + 1 u	73

Number of chocolate cupcakes and vanila cupcakes was equal at first.

1 p + 3 u + 15 = 1 p + 36
3 u = 36 - 15
3 u = 21

1 u = 21 ÷ 3 = 7

Total number of cupcakes 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 = 73
3 p = 73 - 37
3 p = 36

1 p = 36 ÷ 3 = 12

Number of vanila cupcakes at first
= 1 p + 36
= 12 + 36
= 48

Answer(s): 48