Question

Question 85

The sum of three consecutive integers is 5 more than the smallest of the integers. Find the integers.

Answer 1

Let one number be x. Then, the next two consecutive numbers will be x+1 and x+2.
$\therefore$ Sum of these three numbers = x + (x+1) + (x+2) = 3x + 3
According to the question, 3x + 3 = x + 5
$\Rightarrow 3x-x=5-3\left[transposing125toRHS\right]\Rightarrow 2x=2\Rightarrow \frac{2x}{2}=\frac{2}{2}\left[dividingbothsidesby2\right]\Rightarrow x=1$
$\therefore$ Hence, the numbers are 1, 1+1, 1+2 i.e. 1, 2, 3.