Let x be the smaller number. Then the larger number is 2x+1 (since it is greater by 1 than two times the smaller number).
According to the problem, the sum of the two numbers is 37. Therefore, we can write an equation:
x + (2x+1) = 37
Simplifying the left side of the equation:
3x + 1 = 37
Subtracting 1 from both sides:
3x = 36
Dividing both sides by 3:
x = 12
So the smaller number is 12. To find the larger number, we can use the equation we derived earlier:
2x+1 = 2(12) + 1 = 25
Therefore, the two numbers are 12 and 25.