Random Puzzles 

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
From the 1 go straight down.

Answer
 

Workings

Hint
A little bit of algebra might help.

Answer
I have 14 apples and you have 28 apples.

Reasoning
We can work this out with a little algebra. I have A apples and you have B apples, then
[1]  5 x (A – 7) = B + 7

[2]        A + 7 = B – 7

From [1] we have:

    5A – 35 = B + 7
[3]      5A = B + 42

From [2] we have:

[4]  A + 14 = B

We can then use [4] in [3] to give:

  5A = (A + 14) + 42
  5A = A + 56
  4A = 56
   A = 14

Which gives B = 28 (by [4]).

Workings

Hint
The answer involves a square root.

Answer
4.

The middle of each triangle contains the square root of the sum of the three surrounding numbers.