6.Three consecutive integers add up to 51. What are these integers?

Let the three consecutive integers be x, x + 1 and x + 2.
As per the condition given, we have

x + (x + 1) + (x + 2) = 51

\(\Rightarrow\)x + x + 1 + x + 2 = 51

\(\Rightarrow\) 3x + 3 = 51

\(\Rightarrow\) 3x +3 -3= 51 – 3 [subtracting 3 from both the sides]

\(\Rightarrow\)3x = 48

\(\Rightarrow\) x ÷3= 48 ÷ 3 [dividing 3 to both the sides]

\(\Rightarrow\)x = 16

Thus, the required integers are 16, 16 + 1 = 17 and 16 + 2 = 18, i.e., 16, 17 and 18.