Puzzle ZVHV

???

As the auditor for my local theme park, I noticed that on Saturday there were 4296 children and 2143 adults and the takings were £98,718.

However, on Sunday, there were 5146 children and 2807 adults and the takings were £122,570.

How much were the children's tickets and adult's tickets?

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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

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