Question

One number is less than a second number. Five times the first is 1 more than 3 times the second. find the numbers

Answer 1

Let the numbers be represented by "a" and "b".
 a < b
 5a = 1 +3b
Then
 a = (1 +3b)/5
So we can substitute for "a" to gete
 (1 +3b)/5 < b
 1 +3b < 5b
 1 < 2b
 1/2 < b

The conditions will be met for any numbers "a" and "b" such that
 b > 1/2
 a = (1 +3b)/5

Integer solutions will be solutions to the Diophantine equation
 5a -3b = 1
which has solutions (for n ≥ 1)
 a = 3n -1
 b = 5n -2
The smallest pair of integers meeting the requirement is 2 and 3.