Respuesta :
Answer: There are 15 ghosts in a haunted house.
Explanation:
Since we have given that
Total number of ghosts, goblins and ghouls = 51
On Friday,
Let the number of goblins be x
Let the number of ghosts be
[tex]\frac{x}{2}[/tex]
Let the number of ghouls be
[tex]51-x-\frac{x}{2}=51-\frac{3x}{2}[/tex]
On Saturday,
Two-thirds of the ghouls each became a ghost,
So, it becomes
[tex]\frac{2}{3}\times (51-\frac{3x}{2})=34-x[/tex]
Now, number of ghost becomes
[tex]\frac{x}{2}+34-x=34-\frac{x}{2}[/tex]
and number of ghouls becomes
[tex]51-\frac{3x}{2}-34+x=17-\frac{x}{2}[/tex]
On Sunday,
Number of ghosts each became a goblin = 11
So, Number of goblins becomes
[tex]x+11[/tex]
Now, according to question , we have a ratio of ghouls to goblins i.e. 1:3
So, it becomes,
[tex]\frac{17-\frac{x}{2}}{x+11}=\frac{1}{3}\\\\\frac{34-x}{2x+22}=\frac{1}{3}\\\\102-3x=2x+22\\\\102-22=2x+3x\\\\80=5x\\\\\frac{80}{5}=x\\\\16=x[/tex]
So, number of ghosts is given by
[tex]34-\frac{x}{2}-11\\\\=23-\frac{x}{2}\\\\=23-\frac{16}{2}\\\\=23-8\\\\=15[/tex]
So, there are 15 ghosts in a haunted house.
