Today Puzzle #760
Puzzle No. 760鈥� Friday 12 June
The annual fees for the Puzzle Challenge Club are £23 per person, with a special rate for senior citizens of £17. If the total amount of dues collected last year was £1500, what is the smallest number of senior citizens that belong to the club?
Today’s #PuzzleForToday has been set by Dr Steve Humble from Newcastle University
Click here for the answer
There are only 4 possible alternative ways of the club fees being £1500. The alternative with 3 senior citizens is the smallest.
Details of a possible solution.
23X + 17Y = 1500
We can re-write this equation as
X = 12 – 17n and Y = 72 + 23n
where n can take values of 0, -1, -2, -3
Q Y senior X general Senior fees General fees
0 72 12 £1224 £276
-1 49 29 £833 £667
-2 26 46 £442 £1058
-3 3 63 £51 £1449
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