Question

A house was haunted by a combined total of 51 guosts, goblins, and ghouls. On Friday, there were half as many ghosts as there were goblins. On Saturday, two-thirds of the ghouls each became a ghost. On Sunday, 11 of the ghosts each became a goblin, and the ratio of ghouls to goblins became 1 :3. If no other changes occurred, how many ghosts are there?

Answer 1

Answer: There are 15 ghosts in a haunted house.

Step-by-step 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

`(x)/(2)`

Let the number of ghouls be

`51-x-(x)/(2)=51-(3x)/(2)`

On Saturday,

Two-thirds of the ghouls each became a ghost,

So, it becomes

`(2)/(3)* (51-(3x)/(2))=34-x`

Now, number of ghost becomes

`(x)/(2)+34-x=34-(x)/(2)`

and number of ghouls becomes

`51-(3x)/(2)-34+x=17-(x)/(2)`

On Sunday,

Number of ghosts each became a goblin = 11

So, Number of goblins becomes

`x+11`

Now, according to question , we have a ratio of ghouls to goblins i.e. 1:3

So, it becomes,

`(17-(x)/(2))/(x+11)=(1)/(3)\\\\(34-x)/(2x+22)=(1)/(3)\\\\102-3x=2x+22\\\\102-22=2x+3x\\\\80=5x\\\\(80)/(5)=x\\\\16=x`

So, number of ghosts is given by

`34-(x)/(2)-11\\\\=23-(x)/(2)\\\\=23-(16)/(2)\\\\=23-8\\\\=15`

So, there are 15 ghosts in a haunted house.