Largest Sum Puzzle
Starting in the bottom left corner and moving either up or right, adding up the numbers along the way, what is the largest sum that can be made?
Solution (Previous Puzzle):
Adult's tickets were Rs.18 and children's were Rs.14.
This is easily solved using a common method for solving simultaneous equations.
First construct two algebraic equations, where C is the number of children, and A is the number of adults:
4296C + 2143A = 98718 [1]
5146C + 2807A = 122570 [2]
To make the number in front of C the same on both we multiple [1] by 5146 and [2] by 4296 to give:
22107216C + 11027878A = 508002828 [3]
22107216C + 12058872A = 526560720 [4]
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
As required.
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