Mathematical Puzzles 

Workings

Hint

Answer
5 tonnes of chicken feed, 10 tonnes of pig feed and 85 tonnes of cattle feed.

Workings

Hint
There are three feet in a yard, and 1,760 yards in a mile.

Answer
Seconds in a week.

Reasoning
There are 60 x 60 x 24 x 7 = 604,800 seconds in a week.

There are 3 x 1760 x 100 = 528,000 feet in 100 miles.

Workings

Hint
In the first box, look at 7 & 3, and 4 & 1, to see how we can use them to make 12.

Answer
4.

Reasoning
For each row, the left minus the right gives a number.

The numbers for the rows are then multiplied together.

In the first box:

   7 – 3 = 4
   4 – 1 = 3

so 4 x 3 = 12

In the second box:

   9 – 2 = 7
   8 – 3 = 5

so 7 x 5 = 35

In the last box:

   6 – 2 = 4
   8 – 7 = 1

so 4 x 1 = 4.

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