Question

numerele a si b sunt invers proportionale cu numerele 2 si 3 determinati numerele a si b daca 4a+b=28

Answer 1

4a+b=28
$\frac{a}{b}= \frac{2}{3}$
3a=2b
a=$\frac{2}{3}$b
4*$\frac{2}{3}$b+b=28
$\frac{8}{3}$b+b=28
$\frac{8}{3}$b+$\frac{3}{3}$b=28
$\frac{8+3}{3}$b=28
$\frac{11}{3}$b=28
b=28*$\frac{3}{11}  [tex]b= \frac{84}{11}$
a=$\frac{2}{3}$*$\frac{84}{11}$
a=$\frac{56}{11}$

Answer 2

(a;b) i.p.(2;3)
4a+b=28
a/1/2=b/1/3=K ⇔a=K/2
                            b=K/3
4K/2+K/3=28 (simplificam prima fractie cu3 si a doua cu 2 pentru a avea numitor comun )⇔
12K/6+2K/6=28
14K/6=28
14K=28x6
14K=168
K=168:14
K=12
a=12:2=6
b=12:3=4
Verificare:4x6+4=24+4=28