Question

stiind ca nr a,b,c sunt direct proportionale cu nr 0,2; 0,5; 3 ,iar 5a+2b+2c=64,sa se afle numerele.

Answer 1

daca numerele alea sunt direct proportionale,atunci apare ecuatia

a : 0.2 = b : 0.5 = c : 3
5a = 2b = c : 3

Inlocuim in functie de c

5a + 2b + 2c = 2c:3 + 2c = 8c:3 = 64 => c = 24 => a = 8:5 si b = 4

Answer 2

[tex] \frac{a}{b} = \frac{c}{d} =\ \textgreater \ a*d=b*c\\\\ \frac{a}{0,2}= \frac{b}{0,5}= \frac{c}{3} =k\\\\ a= \frac{1}{5} *k\\\\ b= \frac{1}{2} *k\\\\ c=3k\\\\ 5* \frac{1}{5}*k+2* \frac{1}{2} *k+2*3k=64\\\\ k+k+6k=64\\\\ 8k=64\\\\ k= \frac{64}{8}\\\\ \bold{k=8} \\\\ a= \frac{1}{5} *k=\ \textgreater \ a= \frac{8}{5} =\ \textgreater \ \bold{a=1,6}\\\\ b= \frac{1}{2}*k=\ \textgreater \ b= \frac{8}{2}=\ \textgreater \ \bold{b=4} \\\\ c=3*k=\ \textgreater \ c=8*3=\ \textgreater \ \bold{c=24}[/tex]