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Exploring mathematics elementary algebra

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The sum of the of a two-digit number is 15. One third of the number diminished by 12 is 17. Find the number.

  • Exploring mathematics elementary algebra -

    Did you mean the "sum of the digits of a two-digit number is 15" ?
    if so, then
    let the unit digit be x
    let the tens digit be y
    so the value is 10y + x

    "One third of the number diminished by 12 is 17"
    ---> (1/3)(10y+x) - 12 = 17
    (1/3)(10y+x) = 29
    multiply by 3
    10y+x = 87
    x = 87 - 10y

    also x+y = 15
    by substitution:
    87-10y + y = 15
    -9y = -72
    y = 8
    x = 87 - 80 = 7

    the number is 87

    check the properties stated.

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