№19. Реши уравнение, применяя основное свойство пропорции a) 2,57 : x = 28,27 : 15,4; б) 42,6 : 20,59 = y : 7,83; в) a : 5,2 = 22,1 : 1,69; г) 13,4 / 16,75 = 32 / b; д) 3/5 : 1,5 = x : 18/5; е) 2x/3,3 = 4/11; ж) 15 : (x - 5) = 7,5 : 2 1/2; з) 5 3/5 : 7 2/3 = 4 1/2 : (y + 2,3).

a) \(2.57 : x = 28.27 : 15.4\) \(2.57 \cdot 15.4 = 28.27 \cdot x\) \(39.578 = 28.27x\) \(x = \frac{39.578}{28.27}\) \(x = 1.4\) б) \(42.6 : 20.59 = y : 7.83\) \(42.6 \cdot 7.83 = 20.59 \cdot y\) \(333.558 = 20.59y\) \(y = \frac{333.558}{20.59}\) \(y = 16.2\) в) \(a : 5.2 = 22.1 : 1.69\) \(a \cdot 1.69 = 5.2 \cdot 22.1\) \(1.69a = 114.92\) \(a = \frac{114.92}{1.69}\) \(a = 68\) г) \(\frac{13.4}{16.75} = \frac{32}{b}\) \(13.4 \cdot b = 16.75 \cdot 32\) \(13.4b = 536\) \(b = \frac{536}{13.4}\) \(b = 40\) д) \(\frac{3}{5} : 1.5 = x : \frac{18}{5}\) \(\frac{3}{5} : \frac{3}{2} = x : \frac{18}{5}\) \(\frac{3}{5} \cdot \frac{18}{5} = \frac{3}{2} \cdot x\) \(\frac{54}{25} = \frac{3}{2}x\) \(x = \frac{54}{25} \cdot \frac{2}{3}\) \(x = \frac{36}{25}\) или \(x = 1.44\) е) \(\frac{2x}{3.3} = \frac{4}{11}\) \(2x \cdot 11 = 3.3 \cdot 4\) \(22x = 13.2\) \(x = \frac{13.2}{22}\) \(x = 0.6\) ж) \(15 : (x - 5) = 7.5 : 2\frac{1}{2}\) \(15 : (x - 5) = 7.5 : 2.5\) \(15 \cdot 2.5 = 7.5 \cdot (x - 5)\) \(37.5 = 7.5x - 37.5\) \(75 = 7.5x\) \(x = \frac{75}{7.5}\) \(x = 10\) з) \(5\frac{3}{5} : 7\frac{2}{3} = 4\frac{1}{2} : (y + 2.3)\) \(\frac{28}{5} : \frac{23}{3} = \frac{9}{2} : (y + 2.3)\) \(\frac{28}{5} \cdot (y + 2.3) = \frac{23}{3} \cdot \frac{9}{2}\) \(\frac{28}{5}y + \frac{28}{5} \cdot 2.3 = \frac{69}{2}\) \(5.6y + 12.88 = 34.5\) \(5.6y = 21.62\) \(y = \frac{21.62}{5.6}\) \(y = 3.8607\) (приблизительно) Ответ: a) x = 1.4; б) y = 16.2; в) a = 68; г) b = 40; д) x = 1.44; е) x = 0.6; ж) x = 10; з) y = 3.86 (округлено до сотых)