On Friday, a house is haunted by a combined total of 51 ghosts, goblins and ghouls, and there were 1/2 as many ghosts as there were goblins. On Saturday, 2/3 of the ghouls each became a ghost. On Sunday, 11 of the ghosts each became a goblin, and the ratio of ghouls to goblins was then 1/3. At that time how many ghosts were there?

Ghosts Goblins Ghouls Total

Fr 8 16 27 51
Sat 26 16 9 51
Sun 15 27 9 51
33%

15 ghosts

To solve this problem, let's break it down step by step.

Step 1: Write down the given information.
- On Friday, the total number of ghosts, goblins, and ghouls is 51.
- On Friday, the number of ghosts is half the number of goblins.

Step 2: Define variables.
- Let's say the number of ghosts on Friday is G.
- The number of goblins on Friday is 2G (since there are twice as many goblins as ghosts).
- The number of ghouls on Friday is 51 - G - 2G = 51 - 3G.

Step 3: Calculate the number of ghouls on Sunday.
- On Saturday, 2/3 of the ghouls become ghosts, so the remaining 1/3 of the ghouls is left.
- Since the ratio of ghouls to goblins on Sunday is 1/3, we can set up the equation (1/3) * (number of goblins) = (number of ghouls).
- Plugging in the values from Friday, we get (1/3)*(2G) = (51 - 3G).
- Solving this equation, we find 2G/3 = 51 - 3G.

Step 4: Calculate the number of ghosts on Sunday.
- On Sunday, 11 ghosts became goblins, so the remaining ghosts are G - 11.
- Using the information from step 3, we can set up the equation G - 11 = 51 - 3G.
- Solving this equation, we find 4G = 62.
- Dividing both sides by 4, we get G = 62/4 = 15.5.

Step 5: Interpret the result.
- Since we can't have a fraction of a ghost, we can conclude that there were 15 ghosts on Sunday.

Therefore, there were 15 ghosts on Sunday.