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Question Number 92151 by jagoll last updated on 05/May/20
If p and q are positive integers   such that the value   pq + 2p+2q = 217   find p+q
$$\mathrm{If}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}\:\mathrm{are}\:\mathrm{positive}\:\mathrm{integers}\: \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{value}\: \\ $$$$\mathrm{pq}\:+\:\mathrm{2p}+\mathrm{2q}\:=\:\mathrm{217}\: \\ $$$$\mathrm{find}\:\mathrm{p}+\mathrm{q}\: \\ $$
Commented by john santu last updated on 05/May/20
⇒(p+2)(q+2) = 17×13  p+2+q+2 = 30  p+q = 26
$$\Rightarrow\left({p}+\mathrm{2}\right)\left({q}+\mathrm{2}\right)\:=\:\mathrm{17}×\mathrm{13} \\ $$$${p}+\mathrm{2}+{q}+\mathrm{2}\:=\:\mathrm{30} \\ $$$${p}+{q}\:=\:\mathrm{26}\: \\ $$$$ \\ $$

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