Question

the greater of two numbers is 1 less than 4 times the lesser. three times the lesser number is 4 less than the greater. find the numbers

Answer 1

Steps:

So for this, we will be doing a system of equations. Using the info from our question, our two equations are:

(let x = greater number and y = lesser number)

$x=4y-1\\3y=x-4$

Now, for this I will be using the substitution method. Since we know that x = 4y - 1, substitute that into the second equation:

$3y=4y-1-4$

From here we can solve for y. Firstly, combine like terms:

$3y=4y-5$

Next, subtract 4y on both sides of the equation:

$-y=-5$

Next, multiply both sides by -1:

$y=5$

Now that we know the value of y, substitute it into either equation to solve for x:

$x=4(5)-1\\x=20-1\\x=19\\\\3(5)=x-4\\15=x-4\\19=x$

Answer:

In short, 5 is the lesser number and 19 is the greater number.