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
Correct Answer: Option 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