Buying eggs puzzle
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Answered
The cost of eggs at a local shop in Burnley:
- Cost of one snake egg: 5 pence.
- Cost of one Echidna egg: 1 penny
- Cost of 20 Bird eggs: 1 penny
John entered the shop and he need to buy
- All types of eggs.
- birds egg in multiple of 20.
- Total of 100 eggs
How many Snake, Echidna, and Bird eggs does John need to buy considering he got only 100 pence?
Best answer
He has to buy: 19 Snake eggs + 4 sets (20 each) of Birds’ Eggs + 1 Echidna egg.
Calculations:
Assume that he needs to buy ‘b’ sets (20-piece) of Birds’ eggs, ‘e’ number of Echidna eggs and ‘s’ number of Snake eggs.
Cost-wise: b + e + 5s = 100 and – (1)
Number-wise: 20b + e + s = 100 – (2)
(2) – (1)=> 19b – 4s = 0 => s = 19/4 b
Since ‘s’ can’t be a fraction, ‘b’ has to be a multiple of 4. Also, since the max,. number of snake eggs he can buy with 100 pence is 19 (provided he has to buy other eggs also), ‘b’ can’t be more than 4.
Thus, b = 4, s = 19 which leaves 1 penny with which he can buy 1 echidna egg.
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