The Number Game

1,434.6K Views

The product of three consecutive numbers when divided by each of them in turn, the sum of the three quotients will be 74.
What are the numbers?

Share
Add Comment

  • 2 Answer(s)

    4, 5 and 6.

    John123 Expert Answered on 26th July 2015.
    Add Comment

    Let the three consecutive numbers be x, x+1, and x+2.

    When we divide the product of these three numbers by the first number x, we get: (x)(x+1)(x+2)/x = (x+1)(x+2)
    When we divide the product by the second number x+1, we get: (x)(x+1)(x+2)/(x+1) = (x)(x+2)/(x+1)
    When we divide the product by the third number x+2, we get: (x)(x+1)(x+2)/(x+2) = (x)(x+1)
    According to the problem, the sum of these three quotients is 74, so we can write the equation:
    (x+1)(x+2) + (x)(x+2)/(x+1) + (x)(x+1) = 74
    Expanding the terms and simplifying, we get:
    3x^2 + 6x – 72 = 0

    Dividing by 3 and factoring, we get:  x^2 + 2x – 24 = 0
    (x+6)(x-4) = 0

    So x = -6 or x = 4. Since the numbers are consecutive, x must be positive, so x = 4.

    Therefore, the three consecutive numbers are 4, 5, and 6.

    Moshe Expert Answered on 2nd March 2023.
    Add Comment
  • Your Answer

    By posting your answer, you agree to the privacy policy and terms of service.
  • More puzzles to try-