If p,q and r are whole numbers and
p + 1/[(q+1)/r] = 25/19, what is the value of q ?
oh and i forgot to write that the value of q is 3
your equation p + 1/[(q+1)/r] = 25/19
reduces to
p + r/(q+1) = 25/19 and you say that q = 3, so
p + r/4 = 25/19
If p and r are whole numbers, looking at that last equation, there is no way this can happen.
did you make a "typo" ?
To find the value of q, we need to solve the given equation:
p + 1/[(q+1)/r] = 25/19
To simplify the expression 1/[(q+1)/r], we can multiply the numerator and denominator by r:
1/[(q+1)/r] = r/[(q+1)]
Now we can substitute this simplified expression back into the original equation:
p + r/[(q+1)] = 25/19
To further simplify the equation, we need to get rid of the fraction. We can do this by multiplying through by the common denominator, which is (q+1):
19p(q+1) + 19r = 25(q+1)
Expanding both sides:
19pq + 19p + 19r = 25q + 25
Rearranging the terms:
19pq - 25q = 25 - 19p - 19r
Factoring out q:
q(19p - 25) = 25 - 19p - 19r
Finally, solving for q by dividing both sides by (19p - 25):
q = (25 - 19p - 19r) / (19p - 25)
So the value of q is given by the expression (25 - 19p - 19r) / (19p - 25).