Question

Nr a,b sunt invers proportionale cu 5 si 3.Calculati valoarea raportului $\frac{3a+b}{2b-a}$

Answer 1

$\{a,b\}ip\{5,3\}$

$5a=3b=k$

$a=\frac{k}{5}$

$b=\frac{k}{3}$

$\frac{3a+b}{2b-a}=\frac{\frac{3k}{5}+\frac{k}{3}}{\frac{2k}{3}-\frac{k}{5}}=\frac{\frac{14k}{15}}{\frac{7k}{15}}=\frac{15*14k}{15*7k}=\frac{14}{7}=2$

Answer 2

a/1/5=b/1/3
5a=3b=> a=3b/5
 la raport luam pe bucati
numaratorul
3a+b=3x 3b/5+b= 9b/5+b (aduc la acelasi numitor)= 9b/5+5b/5=14b/5
numitorul
2b-a=2b-3b/5 (aduc la acelasi numitor)=2bx5/5-3b/5=10b/5-3b/5= 7b/5
deci raportul (3a+b)/(2b-a)=14b/5/7b/5=14b/5:7b/5=14b/5x5/7b=14b/7b=14/7=2