Respuesta :

-----------------------------------------
Define x :
-----------------------------------------
Let the smallest number be x.
The other two numbers will be x + 1 and x + 2.

-----------------------------------------
Construct Equation :
-----------------------------------------
Sum of these numbers is 72
⇒ x + x + 1 + x + 2 = 72

-----------------------------------------
Solve for x :
-----------------------------------------
x + x + 1 + x + 2 = 72
3x + 3 = 72
3x = 69
x = 23

-----------------------------------------
Find the numbers :
-----------------------------------------
1st number = x = 23
2nd number = x + 1 = 23 + 1 = 24
3rd number = x + 2 = 23 + 2 = 25

----------------------------------------------------------------------------------
Answer : The numbers are 23, 24 and 25.
----------------------------------------------------------------------------------
Consecutive integers are numbers that follow after each other. So 1,2,3,4,5 are consecutive integers

We need 3 consecutive integers that is 72. Note the word is means =

We can set this up like the following: 
x  + (x + 1) + (x+2) = 72
Now combine like terms
x +x + x = 3x
1 + 2  =  3

3x + 3 = 72
Solve for x
3x + 6 = 72
3x = 72 - 3
3x = 69
3x / 3 = 69 / 3
x = 23


Now that we have solved for the first x, which is 23, we plug this into (x + 1) and (x + 2) to solve the other numbers we need

x + (x + 1) + (x + 2) = 72

(x + 1) = (23 + 1) = 24
(x + 2) = (23 + 2) = 25


So we have the following:

x = 23
(x + 1) = (23 + 1) = 24
(x + 2) = (23 + 2) = 25

Our answers are 23, 24, 25, which are consecutive number and when you add them, they = 72