SOLUTION: The sum of four consecutive even integers is 308. Write and solve an equation to find the four integers.

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Question 102354This question is from textbook Algebra
: The sum of four consecutive even integers is 308. Write and solve an equation
to find the four integers. This question is from textbook Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Consecutive even integers follow the form: 2x, 2x%2B2, 2x%2B4, ...., etc.


So the product of four consecutive even integers is:

2x%2B%282x%2B2%29%2B%282x%2B4%29%2B%282x%2B6%29=308


8x%2B12=308 Combine like terms on the left side


8x=308-12Subtract 12 from both sides


8x=296 Combine like terms on the right side


x=%28296%29%2F%288%29 Divide both sides by 8 to isolate x



x=37 Divide

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Answer:
So our answer is x=37




That means our first number is....

2%2837%29=74

So our first number is 74


Our second number is simply 2 more than 74

74%2B2=76

So our second number is 76



Our third number is simply 2 more than 76

76%2B2=78

So our third number is 78


Our fourth number is simply 2 more than 78

78%2B2=80

So our fourth number is 80



So our 4 consecutive even integers are

74,76,78, and 80


Check:

74%2B76%2B78%2B80=308


308=308 works