The sum of three consecutive integers is 48. Find the integers.

Question

Well, guys, I tired and it answer is... What's your answer?!

Let the middle of three consecutive integers be $= X$. Therefore, the other two integers will be $X + 1$ and $x - 1$. By the problem, \begin{align*} (X - 1) + X + X + 1 & = 48\\ X - 1 + X + X + 1 & = 48\\ 3X & = 48\\ X & = 48 \div 3 = 16\\ X - 1 & = 16 - 1 = 15\\ X + 1 & = 16 + 1 = 17 \end{align*}

Therefore, the three consecutive integers $= 15, 16, 17$.

Answer 1

It's not clear how you transform your equation: the three numbers are $x-1$, $x$ and $x+1$, so the equation is $$ (x-1)+x+(x+1)=48 $$ that obviously becomes $$ 3x=48 $$ Since this gives $x=16$, the three numbers are $15$, $16$ and $17$.

Answer 2

The middle term is A.M. of the first and last. Since thrice the middle term is 48, it is 16. Add 1 for next term and subrtract 1 for the previous one.