SOLUTION: What are consecutive numbers? And another question : Find three consecutive even numbers that have a sum of 36. This is confusing!!!!! -Jasmine

Algebra ->  Conversion and Units of Measurement -> SOLUTION: What are consecutive numbers? And another question : Find three consecutive even numbers that have a sum of 36. This is confusing!!!!! -Jasmine      Log On


   

Question 111843: What are consecutive numbers?
And another question : Find three consecutive even numbers that have a sum of 36.
This is confusing!!!!!
-Jasmine
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Consecutive numbers are numbers that follow one another. For instance 3,4,and 5 are consecutive numbers. Consecutive even numbers are even integers that follow one another. So 2,4, and 6 are consecutive even numbers.


So in general, consecutive even numbers follow the form 2x, 2x%2B2, 2x%2B4, etc

So the sum of 3 consecutive even numbers is

%282x%29%2B%282x%2B2%29%2B%282x%2B4%29

Now set the sum equal to 36

%282x%29%2B%282x%2B2%29%2B%282x%2B4%29=36




6x%2B6=36 Combine like terms on the left side


6x=36-6Subtract 6 from both sides


6x=30 Combine like terms on the right side


x=%2830%29%2F%286%29 Divide both sides by 6 to isolate x



x=5 Divide

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Answer:
So our answer is x=5


Now plug in x=5 into 2x


2%285%29=10


So our first number is 10



Now plug in x=5 into 2x%2B2


2%285%29%2B2=10%2B2=12


So our second number is 12




Now plug in x=5 into 2x%2B4


2%285%29%2B4=10%2B4=14


So our third number is 14



Check:
The sum of the numbers should be 36


10%2B12%2B14=36

36=36 and they do. So this verifies our answer.