Question

Question #1f851

Answer 1

The greatest number of the three consecutive odd integers whose sum is 81 is `color(red)(29)`

Explanation:

Let's call the first of the three consecutive odd integers `x`. Then, by definition of "consecutive" and "odd" the other two numbers will be `x + 2` and `x + 4`.

The sum of these three numbers is `81` so we can write:

`x + x + 2 + x + 4 = 81`

`3x + 6 = 81`

`3x + 6 - color(red)(6) = 81 - color(red)(6)`

`3x + 0 = 75`

`3x = 75`

`(3x)/color(red)(3) = 75/color(red)(3)`

`(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = 25`

`x = 25`, this is the first integer.

The other two odd integers are:

`x + 2 = 25 + 2 = 27`

`x + 4 = 25 + 4 = 29`