Let's call the larger number x, and the smaller number y. We know that y is one more than half of x, so we can write y = x/2 + 1. We also know that the sum of the two numbers is 133, so we can write x + y = 133. We can use these two equations to solve for the values of x and y. Substituting the first equation into the second, we get:
x + (x/2 + 1) = 133
Combining like terms, we get:
1.5x + 1 = 133
Subtracting 1 from both sides, we get:
1.5x = 132
Dividing both sides by 1.5, we get:
x = 88
Substituting this value for x in the first equation, we get:
y = 88/2 + 1 = 44 + 1 = 45
Therefore, the two numbers are 88 and 45, and we can check our solution by verifying that the sum of these numbers is indeed 133.
x + y = 88 + 45 = 133
This confirms that our solution is correct.