SOLUTION: Find four consecutive even integers such that twice the sum of the first and fourth is 124.

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Question 221311: Find four consecutive even integers such that twice the sum of the first and fourth is 124.
Answer by drj(1380) About Me  (Show Source):
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Find four consecutive even integers such that twice the sum of the first and fourth is 124.

Step 1. Let n be the first even integer.

Step 2. Let n+2, n+4, and n+6 be the next three consecutive and even integers.

Step 3. Let n+n+6=2n+6 be the sum of the first and fourth even integer

Step 4. Let 2(2n+6) be twice the sum of the first and fourth

Step 5. Then 4(n+3)=124 or

Divide 4 to both sides of the equation

4%28n%2B3%29%2F4=124%2F4

n%2B3=31

Subtract 3 to both sides of the equation

n%2B3-3=31-3

n=28 n%2B2=30 n%2B4=32 n%2B6=34

Check twice of first and fourth integers if equal to 124 or 2*(28+34)=124 which is a true statement.

Step 6. ANSWER: The even and consecutive integers are 28, 30, 32, and 34.

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J