SOLUTION: If p, q, and r are positive integeres and the following is true p + 1/(q + 1/r) = 25/19, then find q.

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Question 80919: If p, q, and r are positive integeres and the following is true p + 1/(q + 1/r) = 25/19, then find q.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
If p, q, and r are positive integers and the following is true:
p + 1/(q + 1/r) = 25/19, then find q.
:
p+%2B+1%2F%28%28q+%2B+%281%2Fr%29%29%29 = 25%2F19
:
1%2F%28%28qr+%2B+1%29%2Fr%29%29%29 = 25%2F19 - p
:
r%2F%28%28qr%2B1%29%29 = 25%2F19 - p, invert fraction when you divide
:
Multiply equation by 19(qr+1) to get rid of the denominators:
19r = 25(qr+1) - P(19(qr+1)
:
19r = 25qr + 25 - (19Pqr + 19P)
:
19r = 25qr + 25 - 19Pqr - 19P
:
19r - 25 + 19P = 25qr - 19Pqr
:
19P + 19r - 25 = q(25r-19Pr)
:
q = %2819P+%2B+19r+-+25%29%2F%2825r-19Pr%29; divided both sides by (25r-19Pr)