three consecutive integers are such that when they are taken in increasing order and multiplied by 2,3,4respectively they add upto 101. Find

Question

three consecutive integers are such that when they are taken in increasing order and multiplied by 2,3,4respectively they add upto 101. Find the number​

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Piper 8 months 2021-09-23T10:28:42+00:00 1 Answer 0 views 0

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    2021-09-23T10:29:51+00:00

    Step-by-step explanation:

    Let x, x+1, x+2 be the consecutive integers.

    2x + 3(x+1) + 4(x+2) = 101

    2x+3x+3+4x+8 = 101

    (2x+3x+4x)+(3+8) = 101

    9x + 11 = 101

    9x = 101 – 11

    9x = 90

    x = \frac{90}{9}

    x = 10

    Since, x = 10, the three integers are 10, 11 and 12

    Check:

    2 x 10 + 3 x 11 + 4 x 12 = 101

    20 + 33 + 48 = 101

    101 = 101

    Conclusion:

    Hence, proved

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