Question 950570
let x = the first number
let y = the second number
We can now turn the word problem into two equations with {{{x}}} and {{{y}}} being the two numbers:
{{{x=3y+18}}} and
{{{x-y=54}}}
Of course, there are 3 ways to solve a system of linear equations: graphing, substitution, and elimination. For this system, I will use substitution.
The first equation already has {{{x}}} isolated so we can just plug the value in to the second equation:
{{{(3y+18)-y=54}}}
{{{2y+18=54}}}
{{{2y=36}}}
{{{y=18}}}
So the smaller number is 18.
Now we can plug the y value back in to the original second equation:
{{{x-18=54}}}
{{{x=72}}}
So the larger number is 72.
The two numbers are 18 and 72.