Question

Numerele a si b sunt invers proportionale cu numerele 2 si 3. Determinati numerele a si b, daca 4a+b=28

Answer 1

2a=3b=> 4a=6b
4a+b=28=>6b+b=28=>7b=28=>b=28/7=>b=4
2a=3b=>2a=12=>a=12/6=>a=2

Answer 2

$\frac{a}{ \frac{1}{2} } = \frac{b}{ \frac{1}{3} }=k   \\ a= \frac{1}{2} k=[tex] \frac{k}{2}$  b= \frac{1}{3} k[/tex]=$\frac{k}{3}$
[tex]4* \frac{k}{2} + \frac{k}{3} =28 \\ 2k+ \frac{k}{3}=28 \\ [/tex]
aducem la acelasi numitor
[tex]6k+k=84 \\ 7k=84 \\ k=12 \\ a= \frac{12}{2} =6 \\ b= \frac{12}{3} =4[/tex]