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

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