From the first statement we know n has to be bigger than 7 (1).
From the second statement we get:
quotient times divisor + remainder is 85.
q * (2n) + (n + 7) = 85 ->
n (2q +1 ) = 78
This simply means that n is a multiple of 78, and the multiplier of it is odd, because (2q + 1) is always odd.
78 = 13 * 3 * 2 * 1
Thus (2q + 1) can be either 1, 3 or 13:
if 2q + 1 is 1 then n is 78 which satisfies (1) - one possible answer
if 2q + 1 is 3 then n is 26 which again satisfies (1) - another possible answer
if 2q+1 is 13 then n has to be 6 which cannot be the case because of the first statement (1)
Thus, 2 possible solutions for n: 78 or 26
From the second statement we get:
quotient times divisor + remainder is 85.
q * (2n) + (n + 7) = 85 ->
n (2q +1 ) = 78
This simply means that n is a multiple of 78, and the multiplier of it is odd, because (2q + 1) is always odd.
78 = 13 * 3 * 2 * 1
Thus (2q + 1) can be either 1, 3 or 13:
if 2q + 1 is 1 then n is 78 which satisfies (1) - one possible answer
if 2q + 1 is 3 then n is 26 which again satisfies (1) - another possible answer
if 2q+1 is 13 then n has to be 6 which cannot be the case because of the first statement (1)
Thus, 2 possible solutions for n: 78 or 26
Statistics : Posted by Vordhosbn • on 26 Jul 2022, 02:24 • Replies 8 • Views 3860
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