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

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Answer 1 · 2018-05-12T17:46:11

The answer is $option A$

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

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,

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