One number is 1 more than 2 times another. their product is 36. find the numbers.

Honestly, this one works out to be a quadratic (which I don't really feel like going into detail) . . . so instead, since this one is fairly simple to think about, I'll simply try "trial and error" . . .

Possible combinations:
1 × 36 = 36
2 × 18 = 36
3 × 12 = 36
4 × 9 = 36
6 × 6 = 36

Obviously, multiply 4 × 2 = 8 . . . and 9 is one more than 8, which is 2 times the first number, 4 . . . so that's your answer . . .

the numbers are 4 and 9

Equations:
b = 2a + 1
a * b = 36 --> a * (2a + 1) = 36 --> 2a^2 + a - 36 = 0
Factor: 
(2a + 9)(a - 4) = 0
2a + 9 = 0 --> a = -9/2 = -4.5
a - 4 = 0 --> a = 4
Assuming a is an integer, then a = 4 so b = 2(4) + 1 = 9
4 and 9