Question

The sum of three consecutive integers is 267. What is the largest integer? find the answers in a numerical form Expected!

Answer 1

To solve this problem, you can use a trick that holds true for every possible triplet of consecutive integers: their sum is always three times the middle number.

In fact, if you call the middle number $x$, the three consecutive numbers are $x-1,\ x,\ x+1$ and their sum is $(x-1)+x+(x+1) = x+x+x-1+1 = 3x$

So, since $\frac{267}{3} = 89$, the middle number is 89. So, the three numbers are 88, 89, 90.