We are given two conditions:

Let x = the first number

Let y = the second number

We are given two conditions:

The first is the numbers have a ratio of 8 to 3 or

Therefore

Another way to write this would be:

The second condition is that they multiply to 864, so:

Substitute for x in the second equation:

Solve for y:

y = +/-18 (reject the negative answer because the problem asks for two positive numbers)

Solve for x by substituting:

Check:

The two numbers are 18 and 48p