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Math Help - Find Larger Number

  1. #1
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    Find Larger Number

    The difference between 2 positive numbers is 9. If 4 times the larger number is 10 times the smaller, what is the larger number?

    Let L = larger number

    Let S = smaller number

    My equations:

    L - S = 9
    4L = 10S

    After doing the math, I came up with the larger number being 90.

    According to the math book, my answer is wrong.

    What did I do wrong?

    Are the equations wrong?

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  2. #2
    Newbie Mirado's Avatar
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    try again

    FYI, I'm not your personal tutor, lol.

    Ok, so if you isolated S and substituted, then you should've gotten  4L = 10 \times (L - 9)

    see what happens with it from there.
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  3. #3
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    Talking

    Quote Originally Posted by magentarita View Post
    The difference between 2 positive numbers is 9. If 4 times the larger number is 10 times the smaller, what is the larger number?

    Let L = larger number

    Let S = smaller number

    My equations:

    L - S = 9
    4L = 10S

    After doing the math, I came up with the larger number being 90.

    According to the math book, my answer is wrong.

    What did I do wrong?
    Since you didn't show your steps in solving, there's no way to know where you might have "done wrong". Sorry!

    Thank you for showing your set-up. Your equations look fine to me. To solve, let's try substitution:

    . . . . .L - S = 9

    . . . . .L = S + 9

    . . . . .4(S + 9) = 10S

    . . . . .4S + 36 = 10S

    . . . . .36 = 6S

    . . . . .6 = S

    Then what must L equal?

    Note that you can check your answer to any "solving" problem by plugging it back into the original exercise. If the larger number were, as you propose, equal to 90, then the smaller number will be 90 - S = 6, or S = 84. But 4(90) = 360, and 10(84) = 840.
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  4. #4
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    Then L =

    Quote Originally Posted by stapel View Post
    Since you didn't show your steps in solving, there's no way to know where you might have "done wrong". Sorry!

    Thank you for showing your set-up. Your equations look fine to me. To solve, let's try substitution:

    . . . . .L - S = 9

    . . . . .L = S + 9

    . . . . .4(S + 9) = 10S

    . . . . .4S + 36 = 10S

    . . . . .36 = 6S

    . . . . .6 = S

    Then what must L equal?

    Note that you can check your answer to any "solving" problem by plugging it back into the original exercise. If the larger number were, as you propose, equal to 90, then the smaller number will be 90 - S = 6, or S = 84. But 4(90) = 360, and 10(84) = 840.

    .L - 6 = 9...Then L = 9 + 6 or 15
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