SOLUTION: I really need your help in solving this problem. I appreciate your time and efforts. Have a terrific evening :) Here is the question? The sum of reciprocals of two consecutive e

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Question 921358: I really need your help in solving this problem. I appreciate your time and efforts. Have a terrific evening :) Here is the question?
The sum of reciprocals of two consecutive even integers is 7/24. Find each integer
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The numbers, 2n and 2n+2. n is any Whole Number.

Transcription becomes 1%2F%282n%29%2B1%2F%282n%2B2%29=7%2F74;
Solve first for n.

SOLVE FOR n.
ORDINARY SKILLS WITH FRACTIONS.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

I really need your help in solving this problem. I appreciate your time and efforts. Have a terrific evening :) Here is the question?
The sum of reciprocals of two consecutive even integers is 7/24. Find each integer


Let smaller integer be S

Then larger = S + 2

Therefore, 1%2FS+%2B+1%2F%28S+%2B+2%29+=+7%2F24

24(S + 2) + 24S = 7(S)(S + 2) ------- Multiplying by LCD, 24S(S + 2)

24S+%2B+48+%2B+24S+=+7S%5E2+%2B+14S

48S+%2B+48+=+7S%5E2+%2B+14S

7S%5E2+%2B+14S+-+48S+-+48+=+0

7S%5E2+-+34S+-+48+=+0

(S - 6)(7S + 8) = 0 

S, or smaller integer = highlight_green%286%29		OR		S = - 8/7 (ignore)

Larger integer: 6 + 2, or highlight_green%288%29

You can do the check!! 

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