SOLUTION: Find four consecutive even numbers which add to 68.

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Question 622633: Find four consecutive even numbers which add to 68.
Found 2 solutions by math-vortex, lenny460:
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--
.
Let x be the first number.
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Then the next three even numbers are x+2, x+4, and x+6.
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The sum of these numbers is 68, so
x%2B%28x%2B2%29%2B%28x%2B4%29%2B%28x%2B6%29=68
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Simplify and solve for x.
4x%2B12=68
4x=68-12
4x=56
x=56%2F4
x=14
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In the context of this problem, the equation x=14 means that the first number is 14. The next three even numbers are 16, 18, and 20.
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Checking we see that 14+16+18+20=68.
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Feel free to email if you still have questions about this.
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Ms.Figgy
math.in.the.vortex@gmail.com

Answer by lenny460(1073) About Me  (Show Source):
You can put this solution on YOUR website!
Let the four consecutive numbers be:
n
n + 2
n + 4
n + 6
Add the above:
n + n + 2 n + 4 + n + 6
Combine like terms:
n + n + n + n = 4n
2 + 4 + 6 = 12
4n + 12 = 68
Subtract 12 from each side of the equation.
4n + 12 - 12 = 68 - 12
Combine like terms:
12 - 12 = 0
68 - 12 = 56
4n = 56
Divide each side by 4
4n/4 = 56/4
n = 14
n + 2 = 14 + 2 = 16
n + 4 = 14 + 4 = 18
n + 6 = 14 + 6 = 20
Therefore the four consecutive numbers are:
14, 16, 18 and 20
obuong3@aol.com