Answer:
(i) Let the number of eggs
given]
If counted in 7, nothing will remain; for some
natural number
If counted in 6, 5 will remain; for some natural
number q (1)
If counted in 5, 4 will remain; for some natural number w (2)
If counted in 4, 3 will remain; for some natural
number s
If counted in 3, 2 will remain; for some natural
number t
If counted in pairs, one will remain; for some natural numbers
That is, in each case, we have a and a positive integer b take values 7, 6,5, 4, 3 and 2 respectively, which divides a and leaves a remainder r (r is 0, 5, 4, 3, 2 and 1, respectively) which is smaller than b.
We must look for the multiple of 7 which satisfy all the conditions. By trial and error (using the concept of LCM), we will find, he had 119 eggs.
(ii) Euclid's division lemma is used to slove the question. (1)
(iii) The value of the trader in the question is honesty. (1)
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