Random Puzzles 

Workings

Hint
Look at the first letters of each word.

Answer
Seals are rare and hungry.

The initial letters spell Sarah. All of the other sentences spell boys' names.

Workings

Hint
The animal begins with the letter F.

Answer
Flamingo.
--ute = flute
c--el = camel
st--g = sting
car-- = cargo

Workings

Hint
It's nothing to do with the word lengths, or vowels.

Answer
Salt.

The initial letters of the words are spelling the word 'PUZZLES'.

Workings

Hint
The answer isn't very large at all.

Answer
There are four boys and six girls in the family.

If there were B boys, and G girls we know that Billy has twice as many sisters as brothers, so 2 x (b − 1) = g.

And his sister, Frankie, has one more sister than she has brothers, so g − 1 = b + 1.
    2(b − 1) = g       [1]
       g − 1 = b + 1   [2]

Using [1] in [2] gives:

2(b − 1) − 1 = b + 1

Expanding the bracket gives:

  2b − 2 − 1 = b + 1

Simplifying the left hand side gives:

     2b − 3  = b + 1

Add 3 to each side gives:

          2b = b + 4

Subtract b from both sides gives:

           b = 4

Using b = 4 in [1] gives:

    2(4 − 1) = g

           6 = g