Question

the greater of two numbers is twice the lesser. If the greater is increased by 18, the result is 4 times the lesser. Find the numbers

Answer 1

Steps:

(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:

`x=2y\ \textsf{(`

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:

`2y+18=4y`

From here we can solve for y. Firstly, subtract 2y on both sides of the equation:

`18=2y`

And next, divide both sides by 2:

`9=y`

Now that we know that the value of y is 9, we can substitute it into either equation to solve for x as such:

`x=2(9)\\x=18\\\\x+18=4(9)\\x+18=36\\x=18`

Answer:

In short, 9 is the lesser number and 18 is the greater number.