If p, q and r are positive integers and p + 1 ⁄ (q + (1 / r)) = 129/31 then what is the value of p + q + r? A. 15 B. 26 C. 31 D. 129 E. 160

1 Answer
May 12, 2018

The answer is #option A#

Explanation:

#p+(1)/(q+1/r)=p+r/(qr+1)=(pqr+p+r)/(qr+1)#

and

#(pqr+p+r)/(qr+1)=129/31#

for #p, q , r in NN#

#qr+1=31#

#qr=30#

Therefore,

#q=6# and #r=5#

And,

#pqr+p+r=129#

#30p+p=124#

#31p=124#

#p=124/31=4#

Finally,

#p+q+r=4+6+5=15#