Answer:

Let's call the smaller number "x" and the larger number "y". We know that y is 3 1/4 times as large as x, so we can write:

y = (13/4)x

We also know that the sum of the two numbers is 102, so we can write:

x + y = 102

Now we can substitute the first equation into the second equation to get:

x + (13/4)x = 102

Multiplying both sides by 4 gives:

4x + 13x = 408

Simplifying the left side gives:

17x = 408

Dividing both sides by 17 gives:

x = 24

Now we can use the first equation to find y:

y = (13/4)x = (13/4) * 24 = 78

Therefore, the two numbers are **24** and **78**.