Answer:
8 ghosts on Friday; 26 ghosts on Saturday; 15 ghosts on Sunday
Explanation:
Let x, y, z represent the numbers of ghosts, ghouls, and goblins on Friday. Their total is 51, and we know x = z/2.
On Saturday the number of ghosts is x +2/3y. and the number of ghouls is y -2/3y = 1/3y. The number of goblins remains unchanged at z.
On Sunday, the number of ghosts is x+2/3y-11; the number of ghouls is still 1/3y; and the number of goblins is z+11. The ratio of ghouls to goblins is 1:3, so ...
... (1/3y) : (z+11) = 1:3
... y = z+11
From this last relationship, and from those that existed on Friday, we can write 3 equations in the 3 unknowns.
- x +y +z = 51
- 2x -z = 0
- y -z = 11
Adding the first equation to each of the last two gives ...
... 3x +y = 51
... x +2y = 62
Subtracting the second from twice the first of these gives ...
... 2(3x +y) -(x+2y) = 2(51) -(62)
... 5x = 40
... x = 8
... 51 -3x = y = 27
... y -11 = z = 16
The number of ghosts changes daily, starting at 8 on Friday, going to 26 on Saturday, and ending at 15 on Sunday.