The sum of 2 positive integers is 151. The lesser number is 19 more than the square root of the greater number, What is the value of the?

The sum of 2 positive integers is 151. The lesser number is 19 more than the square root of the greater number, What is the value of the greater number minus the lesser number?

6 Answers

  • x² + x + 19 = 151

    x² + x – 132 = 0

    x = 11 (valid) or -12 (invalid, as per the question)

    The smaller number is 11+19 = 30 and the greater number is 121.

  • y = 151 – x

    y = x^(1/2) + 19

    151 – x = x^(1/2) + 19

    x^(1/2) = 132 – x

    x = x^2 – 264x + 132^2

    x^2 – 265x + 17424 = 0

    (x – 144)(x – 121) = 0

    Solutions:

    x = 144, y = 7

    x = 121, y = 30

    The numbers are 144 and 7 or 121 and 30

    The value of the greater number minus

    the lesser number is either 137 or 91.

  • A great way to start word problems is to write down everything that is in words in the problem in mathematical terms

    – The sum of 2 positive integers is 151

    (eq1)

    a + b = 151

    – The lesser number is 19 more than the square root of the greater number

    (eq2)

    a – 19 = squareroot(b)

    now you can just plug in. Let’s set equation 2 to b= (I tried a= and it was pretty complicated)

    b = (a-19)(a-19)

    b = a^2 -38a + 361

    and plug that into equation 1

    a + (a^2 -38a + 361) = 151

    set that equation = zero so that we can use the quadratic formula

    a^2 – 37a + 210 = 0

    I leave the quadratic formula to you. Remember that both a and b must be positive, so you should use the positive value, and not the negative value, that you get from the quadratic formula.

    Just plug the value of a into equation 1 to get the value of b.

  • a + b^2 = 151

    a = b + 19

    b + 19 + b^2 = 151

    b^2 + b – 132 = 0

    b = (-1 +/- sqrt(1 + 528)) / 2

    b = (-1 +/- sqrt(529)) / 2

    b = (-1 +/- 23) / 2

    b = -24/2 , 22/2

    b = -12 , 11

    a and b > 0

    b = 11

    b^2 = 121

    a = 30

    30 and 121 are your numbers

  • You have x+y = 115

    and x = 19 + √y or x – 19 = √y.

    Therefore x^2 – 38x + 281 = y – 115 – x

    Solve the quadratic for x.

  • 91

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