# Consecutive Integers

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#### mathdad

##### Full Member
The sum of 3 consecutive integers is 54. DO NOT SOLVE. Set up the needed equation....

Consecutive Integers:

x
x + 1
x + 2

x + (x + 1) + (x + 2) = 54

Yes?

#### pka

##### Elite Member
The sum of 3 consecutive integers is 54. DO NOT SOLVE. Set up the needed equation....

Consecutive Integers:

x
x + 1
x + 2

x + (x + 1) + (x + 2) = 54

Yes?
Yes indeed.

#### Jomo

##### Elite Member
Although you are correct, it is easier to let the numbers be x-1, x and x+1
This way their sum will be (x-1)+x+(x+1) = 3x = 54. So x=18Note how after I did the addition I just had 3x, not for example 3x+7.

Using your method you get (x) + (x+1) + (x+2) = 3x+3 =54. Now you have to deal with the +3.
So 3x =51 and x=17

Can you explain that although both solutions are correct I have different values for x??

• mathdad

#### mathdad

##### Full Member
Although you are correct, it is easier to let the numbers be x-1, x and x+1
This way their sum will be (x-1)+x+(x+1) = 3x = 54. So x=18Note how after I did the addition I just had 3x, not for example 3x+7.

Using your method you get (x) + (x+1) + (x+2) = 3x+3 =54. Now you have to deal with the +3.
So 3x =51 and x=17

Can you explain that although both solutions are correct I have different values for x??
Very good.

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