## pythagoras123 3 years ago 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?

1. integralsabiti

we should also know the remainders.

2. FoolForMath

I am getting 21.

3. integralsabiti

@FoolForMath wanna see your solution pls.

4. beknazar23

82 = n*x + a 90 = m*x + b 168 = k*x + c a+b+c = 25 x - ?

5. integralsabiti

three equasions and 7 variables

6. beknazar23

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

7. FoolForMath

The numbers were small, i simply calculated one by one. The general problem is interesting. I need think about it.

8. beknazar23

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

9. integralsabiti

@beknazar23 s solution is good enough.