Random Puzzles 

Workings

Hints
All of the words are three letters long.

Answers
First set:
bot = small robot bit = small part but = on the contrary bat = nocturnal mammal bet = wager
Second set:
hit = struck het = heated (archaic British) hut = straw dwelling hat = a head warmer hot = not cold

Workings

Hint
What numbers divide into 703?

Answer
The 37 pupils each received 19 sweets.

Reasoning
703 can only be broken down into 19 x 37, it has no other factors.

Workings

Hint
This is quite a tricky puzzle, and knowledge of algebra would certainly help.

Answer
The children tickets were £14, and the adult tickets were £18.

Reasoning
There are a number of methods for solving this problem, including:

Using a spreadsheet. Using a computer program. Using the intersection of lines on a graph. Using an online equation solver. Solving simultaneous equations using algebra. Solving simultaneous equations using inverse matrices.
Here is my solution using simultaneous equations and algebra.

First construct two algebraic equations, where 'c' is the number of children, and 'a' is the number of adults:

[1]   4296c + 2143a = 98718
[2]   5146c + 2807a = 122570

To make the number in front of 'c' the same on both, we multiply [1] by 5146 and [2] by 4296 to give:

[3]   22107216c + 11027878a = 508002828
[4]   22107216c + 12058872a = 526560720

Now we can do [4] − [3] to give:

   1030994a = 18557892

Divide throughout by 1030994 so that:

   a = 18

Substituting a = 18 in [1] will give:

   4296c + 2143 x 18 = 98718
   4296c + 38574     = 98718
   4296c             = 60144
       c             = 14

Double-Checking
c = 14 and a = 18

4,296 x 14 + 2,143 x 18 = 98,718

and

5,146 x 14 + 2,807 x 18 = 122,570

Workings

Hint
Where do the letters of STOP occur in SAFE, STAY, SOON, SKIP?

Answer
POST.

Using the first letter of the first word, the second letter of the second word, etc.