Rael had an equal number of butter biscuits, cream biscuits and blueberry biscuits. After he ate 46 butter biscuits, some cream biscuits and blueberry biscuits, there were 77 biscuits left. The number of cream biscuits he ate was four times the number of blueberry biscuits he ate. The number of cream biscuits left was 22 more than the number of butter biscuits left. How many butter biscuits were there at first?

	Butter biscuits	Cream biscuits	Blueberry biscuits	Total biscuits
Before	1 p + 46	1 p + 4 u + 22	1 p + 4 u + 22
Change	- 46	- 4 u	- 1 u
After	1 p	1 p + 22	1 p + 22 + 1 u	77

Number of cream biscuits and butter biscuits was equal at first.

1 p + 4 u + 22 = 1 p + 46
4 u = 46 - 22
4 u = 24

1 u = 24 ÷ 4 = 6

Total number of biscuits in the end
= 1 p + 1 p + 22 + 1 p + 22 + 6
= 1 p + 1 p + 1 p + 22 + 22 + 6
= 3 p + 50

3 p + 50 = 77
3 p = 77 - 50
3 p = 27

1 p = 27 ÷ 3 = 9

Number of butter biscuits at first
= 1 p + 46
= 9 + 46
= 55

Answer(s): 55