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# 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

A) 3, 4

B) 1, 2

C) 2, 3

D) 0, 1

### 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

## 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