SOLUTION: The sum of the reciprocals of 2 consecutive odd integers is 8/15. Find the numbers.

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Question 1156497: The sum of the reciprocals of 2 consecutive odd integers is 8/15. Find the numbers.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
3 and 5
-
numbers x and x+2;
1%2Fx%2B1%2F%28x%2B2%29=8%2F15
.
4x%5E2-7x-15=0
.
x=%287%2B-+17%29%2F8, generalsolutionquadraticequation


highlight%28x=3%29


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The fraction result does not work for the problem description.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the reciprocals of 2 consecutive odd integers is 8/15. Find the numbers.
Let the smaller odd integer be N

Then the larger odd integer = N + 2

We then get: matrix%281%2C3%2C+1%2FN+%2B+1%2F%28N+%2B+2%29%2C+%22=%22%2C+8%2F15%29

15(N + 2) + 15N, "=", 8N(N + 2) ------ Multiplying by LCD, 15N(N + 2)

matrix%281%2C3%2C+15N+%2B+30+%2B+15N%2C+%22=%22%2C+8N%5E2+%2B+16N%29

matrix%281%2C3%2C+30N+%2B+30%2C+%22=%22%2C+8N%5E2+%2B+16N%29



matrix%281%2C3%2C+4N%5E2+-+12N+%2B+5N+-+15%2C+%22=%22%2C+0%29 ------ Replacing - 7N with - 12N + 5N

4N(N - 3) + 5(N - 3) = 0

(N - 3)(4N + 5) = 0

N, or smaller odd integer = highlight_green%283%29             or           matrix%281%2C4%2C+N%2C+%22=%22%2C+-+5%2F4%2C+%22%28ignore%29%22%29

Do you know what the larger odd integer is now?