Anngela
Answered

Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

. 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 :

pq + pr = 80  => p (q+r) = 80
pq + qr = 425 => q (p+r ) = 425

Factorize 80 with having one factor as prime number
80 =  2 * 40 = 5 *16 

Factrorize 425 with having one factor as prime number
425 = 5 * 85 = 17 * 25...

Therfore, p has to be 2.
q = 17 and r= 23...
p + q +r = 2 + 17+ 23 = 42
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]
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.