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14 November, 18:37

Find three consecutive multiples of 4 so that the product of the first and second number is 16 more than 5 times the third number

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  1. 14 November, 20:30
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    Multiplues of 4 are 4n where n is a natural number

    they numbers are 4n, 4 (n+1), 4 (n+2)

    (4n) (4 (n+1)) = 16+5 (4 (n+2))

    expand

    16n²+16n=16+20n+40

    16n²+16n=56+20n

    divide both sides by 4

    4n²+4n=14+5n

    minus 14+5n both sides

    4n²-n-14=0

    factor

    (n-2) (4n+7) = 0

    set to zero

    n-2=0

    n=2

    4n+7=0

    4n=-7

    n=-7/4, false, n has to be a natural number

    n=2

    so

    4n=8

    4 (n+1) = 12

    4 (n+2) = 16

    the numbers are 8,12,16
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