SOLUTION: sum of three eve consecutive number is 36. find the number

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Question 624660: sum of three eve consecutive number is 36. find the number
Found 2 solutions by lenny460, math-vortex:
Answer by lenny460(1073) About Me  (Show Source):
You can put this solution on YOUR website!
Let the first number be n
Let the second number be n + 2
Let the third number be n + 4

Add all the above together:

n + n + 2 + n + 4 = 36
Combine like terms:
n + n + n = 3n
2 + 4 = 6

Therefore:
3n + 6 = 36
Subtract 6 from each side of the equation
3n + 6 - 6 = 36 - 6
Combine like terms:
6 - 6 = 0
36 - 6 = 30

Therefore:
3n = 30
Divide each side by 3
3n/3 = 30/3
n = 10
n + 2 = 10 + 2 = 12
n + 4 = 10 + 4 = 14

The three consecutive even numbers are:

10, 12 and 14


obuong3@aol.com

Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--

The Problem: 
The sum of three consecutive even numbers is 36. Find the numbers.

Solution:
A sum of consecutive even numbers is series like 2+4+6 or 8+10+12.
Let x be the first even number in the series.

Then the second even number is two more, or x+2.
The third even number is two more than the second, x+2+2 or x+4.

We know that the sum of the three numbers is 36. In algebra, we represent this relationship as
x + x+2 + x+4 = 36

Now we solve this equation for x. First combine like terms. x+x+x is 3x and 2+4 is 6.
3x+6=36

Subtract 6 from both sides of the equation.
3x+6-6=36-6
3x=30

Divide both sides of the equation by 3. 3x/3 is x and 30/3 is 10.
x=10

In the context of this problem, x=10 means that the first even number in the series is 10. The next 
two even numbers are 10+2=12 and 10+4=14.

We need to check that 10,12, and 14 add up to 36.
10+12+14=36 True!

That's it! Please email me if you have questions or comments about the solution. I'm happy to 
explain further and I'd appreciate the feedback.

Ms.Figgy
math.in.the.vortex@gmail.com