(Let x = greater number and y = lesser number)
For this, we will be doing a system of equations. Using the info from the question, our equations are:
[tex]x=2y\ \textsf{("The greater of the 2 numbers is twice the lesser")}\\x+18=4y\ \textsf{("If the greater is increased by 18, the result is 4 times the lesser.")}[/tex]
So for this, I will be doing the substitution method. Since we know that x = 2y, this means we can replace x in the second equation with 2y as such:
[tex]2y+18=4y[/tex]
From here we can solve for y. Firstly, subtract 2y on both sides of the equation:
[tex]18=2y[/tex]
And next, divide both sides by 2:
[tex]9=y[/tex]
Now that we know that the value of y is 9, we can substitute it into either equation to solve for x as such:
[tex]x=2(9)\\x=18\\\\x+18=4(9)\\x+18=36\\x=18[/tex]
In short, 9 is the lesser number and 18 is the greater number.
