Home » Past Questions » Mathematics » The sum of 2 consecutive whole numbers is \(\frac{5}{6}\) of their product, find...

The sum of 2 consecutive whole numbers is \(\frac{5}{6}\) of their product, find...


Question

The sum of 2 consecutive whole numbers is \(\frac{5}{6}\) of their product, find the numbers

Options

A) 3, 4

B) 1, 2

C) 2, 3

D) 0, 1

The correct answer is C.

Explanation:

Let the no. be x and x + 1

x + (x + 1) = \(\frac{5}{6}\) of x(x + 1)

2x + 1 = \(\frac{5}{6}\) x(x + 1)

6(2x + 1) = 5x2 + 5x

12x + 6 = 5x2 + 5x

5x2 + 5x - 12x - 6 = 0

5x2 - 7x - 6 = 0

5x2 - 10x + 3x - 6 = 0

5x(x - 2) + 3(x - 2) = 0

(5x + 3)(x - 2) = 0

(5x + 3)(x - 2) = 0

(5x + 3) = 0

x - 2 = 0

for (5x + 3) = 0

5x = -3

x = \(\frac{-3}{5}\) (Imposible since x is a whole number)

x - 2 = 0

x = 2

x = \(\frac{-3}{5}\)(Impossible since x is a whole number)

x - 2 = 0

x = 2

The numbers are x = 2

x + 1 = 2 + 1

= 3


More Past Questions:


Dicussion (1)

  • Let the no. be x and x + 1

    x + (x + 1) = \(\frac{5}{6}\) of x(x + 1)

    2x + 1 = \(\frac{5}{6}\) x(x + 1)

    6(2x + 1) = 5x2 + 5x

    12x + 6 = 5x2 + 5x

    5x2 + 5x - 12x - 6 = 0

    5x2 - 7x - 6 = 0

    5x2 - 10x + 3x - 6 = 0

    5x(x - 2) + 3(x - 2) = 0

    (5x + 3)(x - 2) = 0

    (5x + 3)(x - 2) = 0

    (5x + 3) = 0

    x - 2 = 0

    for (5x + 3) = 0

    5x = -3

    x = \(\frac{-3}{5}\) (Imposible since x is a whole number)

    x - 2 = 0

    x = 2

    x = \(\frac{-3}{5}\)(Impossible since x is a whole number)

    x - 2 = 0

    x = 2

    The numbers are x = 2

    x + 1 = 2 + 1

    = 3

    Reply
    Like