Today Puzzle #687
Puzzle No. 687鈥� Monday 2 March
A group goes out for lunch at a coffee shop. The bill comes to £171. Each man in the group pays £6 and each woman pays £5 towards the bill. How many different possible groups of men and women could have had lunch at the coffee shop?
Today’s #PuzzleForToday has been set by Dr Steve Humble MBE, Head of Education, Newcastle University
Click here for the answer
Six different possible groups
Details of a possible solution.
6X + 5Y = 171
Re-write this equation as
X = (171 – 5Y)/6 = 28 + (3 – 5Y)/6
Let P = (3-5Y)/6 and Y = -P + (3 – P)/5
If we now let Q = (3 – P)/5 this gives
X = 31 – 5Q and Y = 6Q – 3
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