Question

Question #35603

Answer 1

`7,8,9`

Explanation:

`"note that "color(blue)"consecutive integers"" have a difference"`
`"of one unit between them"`

`"let the first integer "=n`

`"then the second integer "=n+1`

`"and the third integer "=n+2`

`"twice the first added to the last "=2n+n+2`

`"expressing the statement as an equation"`

`2n+n+2=23`

`rArr3n+2=23`

`"subtract 2 from both sides"`

`3ncancel(+2)cancel(-2)=23-2`

`rArr3n=21`

`"divide both sides by 3"`

`(cancel(3) n)/cancel(3)=21/3`

`rArrn=7`

`rArrn+1=7+1=8`

`rArrn+2=7+2=9`

`"the three consecutive integers are "7,8" and "9`

`color(blue)"As a check"`

`(2xx7)+9=14+9=23to" Correct"`

Answer 2

The three integers are 7, 8 and 9.

Explanation:

I used trial and error which was based on a rough equation.

Let's say the integers are `x , y and z.`

`2x + z = 23`

Substitute `z = 9` (using trial and error)

`2x + 9 = 23`

`2x = 14`

`x = 7`