Question

The sum of 3 consecutive numbers is 72. What are the smallest of these numbers?

Answer 1

let's say, we have three numbers, they're consecutive, that simply means that to get the next one, we simply either, add or subtract one from the current one. So if the first number is say 7, the next consecutive must be either 7-1 or 6, or 7+1 or 8, 6, 7 and 8 are consecutive indeed.

so let's say our first number is a, the next one will then be a + 1, and the one after that will be a + 1 + 1 or a + 2.

we know their sum is 72, therefore.

`\bf \stackrel{\textit{first number}}{(a)}+\stackrel{\textit{second number}}{(a+1)}+\stackrel{\textit{third number}}{(a+2)}~~=~~72 \\\\[-0.35em] ~\dotfill\\\\ 3a+3=72\implies 3a=69\implies a=\cfrac{69}{3}\implies a=23 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{a}{23}\qquad \stackrel{a+1}{24}\qquad \stackrel{a+2}{25}~\hfill`

and the smallest is of course, the first one.

Answer 2

23, 24, 25 --> 23 is the smallest

23+24 = 47+25 = 72