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Math Help - Verbal Problem

  1. #1
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    Exclamation Verbal Problem

    can someone please help me with this verbal problem?

    The sum of 3 consecutive integers is 75 less than 5 times the smallest integer. Find the LARGEST of the integers.

    thx
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  2. #2
    Senior Member eumyang's Avatar
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    n + (n + 1) + (n + 2) = 5n - 75
    Solve for n; the largest integer would be n + 2.
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  3. #3
    Junior Member bondesan's Avatar
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    Let a, b, c be three consecutive integers with a < b < c. So we have:

    The sum of 3 consecutive integers: a + b + c

    (Is) 75 less than 5 times the smallest integer: 5a - 75

    So we have: a + b + c = 5a - 75.

    If a, b and c are consecutives, and as we choose "a" as the smallest integer, then b = a+1 and c = a+2.
    Thus: a + b + c = 5a - 75 => a + (a+1) + (a+2) = 5a - 75

    3a + 3 = 5a - 75
    -2a = -78
    a = 39

    The largest integer is c, wich is a + 2, so c = 41.
    Last edited by bondesan; July 26th 2010 at 07:29 PM.
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  4. #4
    Senior Member eumyang's Avatar
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    Quote Originally Posted by bondesan View Post
    (Is) 75 less than 5 times the smallest integer: 75 - 5a
    When translating the phrase "less than" for subtraction, you have to change the order of numbers, so it's 5a - 75 and not 75 - 5a.
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  5. #5
    Junior Member bondesan's Avatar
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    Quote Originally Posted by eumyang View Post
    When translating the phrase "less than" for subtraction, you have to change the order of numbers, so it's 5a - 75 and not 75 - 5a.
    Indeed, thanks for the advice. I'll correct it.
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