pythagoras123
  • pythagoras123
The numbers 82, 90 and 168 are divided by a positive integer (a non-zero whole number), leaving remainders. If the sum of the three remainders is 25, what is the positive integer?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
we should also know the remainders.
anonymous
  • anonymous
I am getting 21.
anonymous
  • anonymous
@FoolForMath wanna see your solution pls.

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anonymous
  • anonymous
82 = n*x + a 90 = m*x + b 168 = k*x + c a+b+c = 25 x - ?
anonymous
  • anonymous
three equasions and 7 variables
anonymous
  • anonymous
you should add theses 3 equations, then you'll get: 340 = x*(n+m+k)+ 25, replace n+m+k = c(some positive integer like x) 315 = x*c
anonymous
  • anonymous
The numbers were small, i simply calculated one by one. The general problem is interesting. I need think about it.
anonymous
  • anonymous
my equation helps to reduce the candidate numbers: x = 3,5,7,21 only. because, there are only integer number. then you'll put these candidate numbers one-by-one
anonymous
  • anonymous
@beknazar23 s solution is good enough.

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