Three consecutive integers have a sum of 57 . Find the integers.

Question

Three consecutive integers have a sum of
57
. Find the integers.

Answer 1

Hello, Rosalyn,

     "Consecutive"  means that the integers will follow each other in value, for example:  1, 2, 3 or 4, 5, 6.  Also, no decimals are needed here because "integers" are whole, counting numbers.

 

Here is the set up:   Let x= the first integer     Then    X+1= 2nd consecutive integer   and x+2= 3rd  .  

Suppose that x=1   x+1= 1+1=2   and x+2=1+2=3   However, you need specific consecutive numbers whose sum is 57.  Remember that sum means to add:

 

x+  (x+1)  + (x+2) = 57                 Addition of all 3 consecutive numbers   Now solve for x

                                                    and substitute into each part to come up with the three integers:

 

3x + 3= 57        3x=54               x=54/3  =  18            x=18,   x+1= 18+1=19      x+2=18+2=20

 

Check your answer:  18+19+20=57                 57=57  Check   

I hope that I have helped.                                 Susan C.       

Answer 2

Hello Rosalyn,

Let x = the first integer 
Let x + 1 = the second integer
Let x + 2 = the third integer

Now write an equation: 

x + (x + 1) + (x + 2) = 57

Combine like terms: 

3x + 3 = 57 

3x = 57 - 3

3x = 54 

x = 18 

Now substitute: 

x = 18
x + 1 = 19 
X + 2 = 20 


Your consecutive integers are 18, 19, and 20 

Hope this helps. 

Answer 3

Let the 3 consecutive integers be

 

n

n + 1

n + 2

 

Then

 

n + (n + 1) + (n + 2) = 57

 

3n + 3 = 57

 

n = (57 - 3)/3 = 54/3 = 18

 

The integers are

 

18

18 + 1 = 19

18 + 2 = 20

 

Test the answers.