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    blazin420's Avatar
    blazin420 Posts: 1, Reputation: 1
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    #1

    Oct 5, 2009, 02:47 AM
    verbal expression, consecutive even integers
    four times the lesser of two consecutive even integers is 12 less than twice the greater number. Find the integers.
    ArcSine's Avatar
    ArcSine Posts: 969, Reputation: 106
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    #2

    Oct 5, 2009, 03:57 AM
    Any even integer can be written in the form 2k, where k is an integer. For example, 32 is 2k, where k is 16; -18 is 2k where k is -9.

    Let your "two consecutive even integers" be 2k and 2k + 2. Then your word problem sets up as

    4(2k) + 12 = 2(2k + 2)

    Solve for k, and then you can easily determine your two integers. Be sure to test your proposed answer back into the problem before you call it a day.
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #3

    Oct 5, 2009, 08:48 AM

    I find it easier to think of the smaller number as N and the larger as N+2. Then the problem becomes

    4* smaller = 2 * larger -12
    4N = 2(N+2)-12
    Solve for N.
    ArcSine's Avatar
    ArcSine Posts: 969, Reputation: 106
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    #4

    Oct 5, 2009, 10:50 AM
    Roger that... using N instead of 2k for the lesser of the two integers certainly gives an easier set-up, and simpler algebra. I just used 2k so that the original model would be respecting the problem's stated "even" integer requirement right from the get-go. Overkill in this case, sure; just a habit of being overly cautious when I'm getting one teed up, before I take a swing at it.

    Adios, gentlemen, and have a nice one...
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