Answered

Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

The prime numbers p, q, r satisfy the simultaneous equations
pq + pr = 80 and pq + qr = 425. Find the value of p + q + r.

Sagot :

Icuk18sugiarto
[tex]first\ equation :\\pq+pr=80\\pq=80-pr..........[1]\\\\secon\ equation :\\pq+qr=425..........[2][/tex]

[tex]Now\ substituting\ equation\ 1\ into\ 2:\\\\pq+qr=425\\(80-pr)+qr=425\\-pr+qr=425-80\\-pr+qr=345\\r(q-p)=345\\\\we\ have :\\ p(q+r)=80=2^{4} \times 5,\\q(p+r)=425=5^{2} \times 17\\r(q-p)=345=3 \times 5 \times 23\\\\so\ : p = 2\ or\ 5, ~q=5\ or\ 17,~ r = 3,5,or\ 23.[/tex]

[tex]From\ : p(q+r)=80, if~p=5~then\ q+r=16, which\ has\ no\ solution\\So~~p=2, then\ ~q+r=40, hence~~q=17~~and~~r=23.\\\\\therefore~~ p+q+r~~~is~~~\boxed{2+17+23=42}[/tex]
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.