Let a, b, c, and n be positive integers. If a + b + c = 19 *97 and a+n=b-n=c/n; compute value of a

Question

rational · Answer

a+n = c/n
b-n = c/n
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a+b = 2c/n

a+b+c = 19*97
2c/n + c = 19*97

(n+2)*c/n = 19*97

rational · Answer

Next notice that the right hand side is a product of two "primes", so there are only finite number of combinations for the left hand side product. Work them by cases

rational · Answer

letting n+2 = 19 and c/n = 97 gives you a = 80

anonymous · Answer

n=17 then

rational · Answer

coincidence the answer i got in below question is also 80 ! http://openstudy.com/study#/updates/55046957e4b079ad354fc2af