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

3, 4

1, 2

2, 3

0, 1

Correct answer is C

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

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