Question

Numerele a,b s c sunt invers proportionale cu 2,3 si 4. Daca 6a+9b-4c= 75,determinati numerele a b si c.
Repedeeee!

Answer 1

[tex]\{a,b,c\}i.p.\{2,3,4\}\Rightarrow \frac{a}{\frac{1}{2}}=\frac{b}{\frac{1}{3}}=\frac{c}{\frac{1}{4}}=k\Rightarrow a=\frac{k}{2}, b=\frac{k}{3}, c=\frac{k}{4}\\ 6a+9b-4c=75\\ 6\cdot\frac{k}{2}+9\cdot\frac{k}{3}-4\cdot \frac{k}{4}=75\\ 3k+3k-k=75\\ 5k=75\Rightarrow \boxed{k=15}\\ a=\frac{k}{2}\Rightarrow \boxed{a=\frac{15}{2}}\\ b=\frac{k}{3}\Rightarrow \boxed{b=5}\\ c=\frac{k}{4}\Rightarrow \boxed{c=\frac{15}{4}}[/tex]