Question

Numerele a si b sunt invers proportionale cu 5 si 3.Calculati valuarea raportului 3a+b supra 2b-a

Answer 1

a,b  ip cu 5,3
5a=3b=k
a=k/5
b=k/3

3a+b  supra 2b-a
3k/5 +k/3  supra 2k/3- k/5
(9k+5k)/15  supra (10k-3k)/15
14k/15  supra 7k/15
14k/15 *15/7k=2/1=2

Answer 2

$5a=3b\Rightarrow \dfrac ab=\dfrac35.$

Simplificam fractia data cu b si obtinem

$\dfrac{3a+b}{2b-a}=\dfrac{3\cdot\dfrac ab+1}{2-\dfrac ab}=\dfrac{3\cdot\dfrac35+1}{2-\dfrac35}=\dfrac{\dfrac{14}{5}}{\dfrac75}=\dfrac{14}{5}\cdot\dfrac57=2$