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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

1 Answer

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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.

User Stormwild
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