Question

Given m and n are two natural numbers. 

290 = 5 m + 3 n + m n

Calculate n/m.

Answer 1

MATHEMATICAL GENERALITY -

GIVEN -

290 = 5m + 3n + mn

290 = n ( 3 + m ) + 5m

290 = n ( m + 3 ) + 5m

For natural numbers , now generality comes , accordingly , let's take m = 2

290 = n ( 3 + m ) + 5m

290 = n ( 3 + 2 ) + 5m

290 = n ( 5 ) + 10

5n + 10 = 290

5n = 290 - 10 = 280

5n = 280

Therefore , n = 280/5 = 56

n = 56 , m = 2 Is perfectly perfect here ,

HENCE , n/m = 56 / 2 = 28

Answer 2

Hello respected sir ^_^!!
This is Aishwary

5m + 3n + mn= 290
adding 15 on both the side , to get

15 + 5m + 3n+ mn= 290 +15

5 ( 3+ m) + n( 3+m) = 305

( 5+n) ( 3+m) = 305

( 5+n) ( 3+m) = 5×61. ( As 305 can be expressed in its primes form)
comparing both the side

5 +n = 61
n= 56

and also , 3 +m= 5 => 2

As the question given condition is that
n/m
so
56/2 = 28
Hence , 28 is the desired answer