Question

Suma a trei numere este 345.Daca se mareste primul cu 25% din el,al doilea cu 50% din el,al treilea cu 30% din el.Numerele devin egale.Calculati numerele.

Answer 1

a+b+c=345
[tex]a+ \frac{25}{100} *a=b+ \frac{50}{100} *b=c+ \frac{30}{100} *c=> \frac{5a}{4} = \frac{3b}{2}= \frac{13c}{10} [/tex]
$\frac{5a}{4} = \frac{3b}{2} => 10a=12b=> a= \frac{12b}{10}= \frac{6b}{5}$
$\frac{3b}{2}= \frac{13c}{10} => 30b=26c=> c= \frac{30b}{26} = \frac{15b}{13}$
Inlocuim in prima relatie si obtinem:
$\frac{6b}{5} +b+ \frac{15b}{13} =345=> \frac{6b*13+65b+15b*5}{65}=345=> 218b= 65*345$=> b=$\frac{22425}{218}$=> $a= \frac{26910}{218} , c= \frac{25875}{218}$