To find the values of x and y, we can create a system of equations using the given information:

1) x + y = 48
2) x * y = 15

From equation 1, we can rearrange it to get y = 48 - x.

Substitute this expression for y into equation 2:

x * (48 - x) = 15
48x - x^2 = 15
x^2 - 48x + 15 = 0

Now we can solve this quadratic equation for x using the quadratic formula:

x = [48 ± sqrt((48)^2 - 4115)] / 2
x = [48 ± sqrt(2304 - 60)] / 2
x = [48 ± sqrt(2244)] / 2
x = [48 ± 47.43] / 2

So, x = 48 + 47.43, x = 48 - 47.43

x = 95.43 / 2 or x = 0.57 / 2

Therefore, x = 47.715 or x = 0.285.

To find the values of y, we substitute these values of x back into y = 48 - x:

If x = 47.715, then y = 48 - 47.715 = 0.285.
If x = 0.285, then y = 48 - 0.285 = 47.715.

So, x = 47.715, y = 0.285
or x = 0.285, y = 47.715.