Question

The sum of three consecutive integers is 75, what are the integers?

Answer 1

Three consecutive integers can be written as `(x) , (x+1) , (x+2)`

Adding them:
`(x) + (x+1) + (x+2) = 75`
`3x +3 = 75`
`3x = 75 - 3 = 72`
`color(purple)(x = 72/ 3 = 24`

so ,`x+1 = 25 , x+ 2 = 26`

the numbers are `color(purple)(24,25,26`

Answer 2

This is the type of puzzle that we should try to perform as mental math (in your head). The answer is `24, 25, 26.`

Explanation:

To arrive at this answer, we can avoid a lot of math formulas, and the use of a calculator by investigating the given statement and quantities.

Three consecutive integers means three numbers that follow each other like `1,2,3.` So if we add these up we get `6` as a sum.

But in this case the desired sum of three consecutive integers is `75`.
That means we can start by dividing the target sum `75` by `3`.

`75/3= 25to` you have probably memorized that one already.

That means `3xx25=75 or 25+25+25=75`

But if we take a `1` from the first `25` and move it to the third `25`, we arrive at:

`24,25,26to` which are three consecutive integers that sum to 75#.

If you can understand this method and are careful in using it you will save a lot of time when these types of puzzles appear.