Question

va rog mult dau coronița!!!!!!:)​

Answer 1

$a) \: \tfrac{2}{5} = \tfrac{x}{10} \implies \: x = \tfrac{2 \times 10}{5} = 10 \\ \sout{ - - - - - - - - - - - - - - - } \\ b) \: \tfrac{6}{x} = \tfrac{4}{5} \implies \: x = \tfrac{6 \times 5}{4} = 7.5 \\\sout{ - - - - - - - - - - - - - - - } \\ c) \: \tfrac{2 + 6 \times 9}{12} = \tfrac{x}{5} \implies \: x = \tfrac{5 \times 56}{12} = \tfrac{70}{3} \\ \sout{ - - - - - - - - - - - - - - - } \\ d) \: \tfrac{20 - 20:10 }{x} = \tfrac{4}{9} \\ \\ \implies x = \tfrac{9(20 - 10)}{4} \\ \implies x = \tfrac{9 \times 10}{4} \\ \implies x = 22.5 \\ \sout{ - - - - - - - - - - - - - - - } \\ e) \: \tfrac{6}{x} = \tfrac{100}{1 + 2 + 3 + ... + 99} \\ \\ \implies100x = 6(1 + 2 + 3 + ... + 99) \\ \implies100x = 6 \cdot \tfrac{99\cdot100}{2} \\ \implies100x = 3\cdot99\cdot100 \\ \implies x = 3\cdot99 \\ \implies x = 297$

Answer 2

$a)~\cfrac{2}{5} =\cfrac{x}{10} \Rightarrow 2 \cdot 10=5x \Rightarrow 5x=20 \Rightarrow x=\cfrac{20}{5}\Rightarrow x=4\\\\b)~\cfrac{6}{x}=\cfrac{4}{5} \Rightarrow 6 \cdot 5=4x \Rightarrow 4x=30 \Rightarrow x=\cfrac{30}{4} \Rightarrow x=\cfrac{15}{2} \\\\c)~\cfrac{2+6\cdot 9}{12}=\cfrac{x}{5} \Rightarrow \cfrac{2+54}{12} =\cfrac{x}{5} \Rightarrow \cfrac{56}{12} =\cfrac{x}{5}\Rightarrow 56 \cdot 5 =12x \Rightarrow \\\\\Rightarrow 12x=280 \Rightarrow x=\cfrac{280}{12}\Rightarrow x=\cfrac{70}{3}$

$d)~\cfrac{20-20:10}{x} =\cfrac{4}{9} \Rightarrow \cfrac{20-2}{x} =\cfrac{4}{9} \Rightarrow \cfrac{18}{x} =\cfrac{4}{9} \Rightarrow 18 \cdot 9=4x \Rightarrow \\\\\Rightarrow 4x=162 \Rightarrow x=\cfrac{162}{4} \Rightarrow x=\cfrac{81}{2} \\\\e)~\cfrac{6}{x} =\cfrac{100}{1+2+3+...+99} \Rightarrow \cfrac{6}{x} =\cfrac{100}{\cfrac{99(99+1)}{2} }\Rightarrow \cfrac{6}{x} =\cfrac{100}{\cfrac{99 \cdot 100}{2} } \Rightarrow$

$\Rightarrow \cfrac{6}{x} =\cfrac{1}{\cfrac{99}{2} }\Rightarrow \cfrac{6}{x} =1 \cdot \cfrac{2}{99} \Rightarrow \cfrac{6}{x} =\cfrac{2}{99} \Rightarrow 6 \cdot 99=2x \Rightarrow 2x=594 \Rightarrow \\\\\Rightarrow x=\cfrac{594}{2} \Rightarrow x=297$