The sum of three consecutive even numbers is 36. Find the numbers.
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.
Subtract 6 from both sides of the equation.
Divide both sides of the equation by 3. 3x/3 is x and 30/3 is 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.
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