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Suma a 3 numere este 505 . Daca s-ar adauga la primul 1/ 7din el la al doilea 0,(1) din el si la al treilea 0,(3) din el , s-ar obtine numere egale. Aflati numerele.

Răspuns :

Danamocanu71
a+b+c=505;
1/7·a+a=1/9·b+b=3/9·c+c;
⇒1/7·a+a=1/9·b+b=1/3·c+c;
⇒a/7+a=b/9+b=c/3+c;
⇒a/7+7a/7=b/9+9b/9=c/3+3c/3
⇒8a/7=10b/9=4c/3;
⇒8a/7=10b/9=4c/3=k
⇒8a/7=k⇒a=7k/8;
⇒10b/9=k⇒b=9k/10;
⇒4c/3=k⇒c=3k/4;
⇒7k/8+9k/10+3k/4=300
⇒35k/40+36k/40+30k/40=300
⇒101k/40=300
⇒k=40·300/101
⇒k=118,[8118]
⇒a=103,[9603];
⇒b=106,[9306];
⇒c=89,[10891];

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