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

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

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Answers ( No )

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    2021-10-04T11:52:13+00:00

    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{("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.")}

    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.

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