Question 128191
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 {{{8/3}}}
Therefore {{{x/y = 8/3}}}
Another way to write this would be:
{{{x = 8y/3}}}
The second condition is that they multiply to 864, so:
{{{x*y = 864}}}
Substitute for x in the second equation:
{{{(8y/3)*y = 864}}}
Solve for y:
{{{8y^2/3 = 864}}}
{{{8y^2 = 2592}}}
{{{y^2 = 324}}}
y = +/-18 (reject the negative answer because the problem asks for two positive numbers)
{{{y = 18}}}
Solve for x by substituting:
{{{x*y = 864}}}
{{{x*18 = 864}}}
{{{x = 48}}}

Check:
{{{x = 8y/3}}}
{{{48 = 8(18)/3}}}
{{{48 = 144/3}}}
{{{48 = 48}}}

The two numbers are 18 and 48