Question

Testul 3 ex 1 dau coroana​

Answer 1

$\displaystyle a)~\frac{5}{\cfrac{1}{2}+\cfrac{1}{3} } =\frac{x}{12} \Rightarrow \frac{5}{\cfrac{3+2}{6} } =\frac{x}{12} \Rightarrow \frac{5}{\cfrac{5}{6} } =\frac{x}{12} \Rightarrow 5 \cdot \frac{6}{5} =\frac{x}{12} \Rightarrow 6=\frac{x}{12} \Rightarrow \\\\ \Rightarrow 6 \cdot 12=x \Rightarrow x=72$

$\displaystyle b)~\frac{0,(3)}{0,3(8)} =\frac{x-1}{1,1(6)} \Rightarrow \frac{\cfrac{3}{9} }{\cfrac{38-3}{90} } =\frac{x-1}{\cfrac{116-11}{90} } \Rightarrow \frac{\cfrac{3}{9} }{\cfrac{35}{90} } =\frac{x-1}{\cfrac{105}{90} } \Rightarrow \\\\ \Rightarrow \frac{3}{9} \cdot \frac{90}{35} =(x-1) \cdot \frac{90}{105} \Rightarrow \frac{6}{7} =\frac{6(x-1)}{7} \Rightarrow \frac{6}{7}=\frac{6x-6}{7}\Rightarrow\\\\ \Rightarrow 6=6x-6 \Rightarrow -6x=-6-6 \Rightarrow -6x=-12 \Rightarrow x=\frac{12}{6} \Rightarrow x=2$