№21. Реши уравнения: 1) 5,4 : a = 1,8 : 6,8; 2) b : 6 5/7 = 5 4/9 : 4 2/3; 3) 720/91,2 = c/0,513; 4) 4,2/7 7/9 = 3 1/9/d; 5) 2,4 : (0,5k) = 3,6 : 1 1/3; 6) 7 : (7/11m) = 56 : 3,2; 7) 8/9 = 6,4/(0,45); 8) 2,1/27 = 2 2/3/0,3p; 9) 4 : (x-3) = 2 : 3; 10) (2y+1,6)/0,8 = 30/2,5; 11) 1,5/(4x-1) = 0,4/(x+4); 12) (5y/1 1/3) = (y-0,9)/0,2

1) \(5.4 : a = 1.8 : 6.8\) \(5.4 \cdot 6.8 = 1.8a\) \(36.72 = 1.8a\) \(a = \frac{36.72}{1.8}\) \(a = 20.4\) 2) \(b : 6\frac{5}{7} = 5\frac{4}{9} : 4\frac{2}{3}\) или \(b : \frac{47}{7} = \frac{49}{9} : \frac{14}{3}\) \(b \cdot \frac{14}{3} = \frac{47}{7} \cdot \frac{49}{9}\) \(b \cdot \frac{14}{3} = \frac{329}{9}\) \(b = \frac{329}{9} \cdot \frac{3}{14}\) \(b = \frac{329}{42}\) или \(b = 7.83\) (приблизительно) 3) \(\frac{720}{91.2} = \frac{c}{0.513}\) \(720 \cdot 0.513 = 91.2c\) \(369.36 = 91.2c\) \(c = \frac{369.36}{91.2}\) \(c = 4.05\) 4) \(\frac{4.2}{7\frac{7}{9}} = \frac{3\frac{1}{9}}{d}\) или \(\frac{4.2}{\frac{70}{9}} = \frac{\frac{28}{9}}{d}\) \(4.2 \cdot d = \frac{70}{9} \cdot \frac{28}{9}\) \(4.2d = \frac{1960}{81}\) \(d = \frac{1960}{81} \cdot \frac{1}{4.2}\) \(d = 5.76\) (приблизительно) 5) \(2.4 : (0.5k) = 3.6 : 1\frac{1}{3}\) или \(2.4 : 0.5k = 3.6 : \frac{4}{3}\) \(2.4 \cdot \frac{4}{3} = 0.5k \cdot 3.6\) \(3.2 = 1.8k\) \(k = \frac{3.2}{1.8}\) \(k = 1.78\) (приблизительно) 6) \(7 : (\frac{7}{11}m) = 56 : 3.2\) \(7 \cdot 3.2 = \frac{7}{11}m \cdot 56\) \(22.4 = \frac{392}{11}m\) \(m = 22.4 \cdot \frac{11}{392}\) \(m = 0.628\) (приблизительно) 7) \(\frac{8}{9} = \frac{6.4}{0.45}\) \(8 \cdot 0.45 = 9 \cdot 6.4\) \(3.6 = 57.6\), это не уравнение, а проверка равенства и оно неверное. 8) \(\frac{2.1}{27} = \frac{2\frac{2}{3}}{0.3p}\) или \(\frac{2.1}{27} = \frac{8/3}{0.3p}\) \(2.1 \cdot 0.3p = 27 \cdot \frac{8}{3}\) \(0.63p = 72\) \(p = \frac{72}{0.63}\) \(p = 114.29\) (приблизительно) 9) \(4 : (x - 3) = 2 : 3\) \(4 \cdot 3 = 2(x - 3)\) \(12 = 2x - 6\) \(18 = 2x\) \(x = 9\) 10) \(\frac{2y + 1.6}{0.8} = \frac{30}{2.5}\) \((2y + 1.6) \cdot 2.5 = 0.8 \cdot 30\) \(5y + 4 = 24\) \(5y = 20\) \(y = 4\) 11) \(\frac{1.5}{4x - 1} = \frac{0.4}{x + 4}\) \(1.5(x+4) = 0.4(4x - 1)\) \(1.5x + 6 = 1.6x - 0.4\) \(6.4 = 0.1x\) \(x = 64\) 12) \(\frac{5y}{1\frac{1}{3}} = \frac{y - 0.9}{0.2}\) или \(\frac{5y}{4/3} = \frac{y - 0.9}{0.2}\) \(\frac{15y}{4} = \frac{y - 0.9}{0.2}\) \(0.2 \cdot 15y = 4(y - 0.9)\) \(3y = 4y - 3.6\) \(y = 3.6\) Ответ: 1) a = 20.4; 2) b = 7.83 (приблизительно); 3) c = 4.05; 4) d = 5.76 (приблизительно); 5) k = 1.78 (приблизительно); 6) m = 0.628 (приблизительно); 7) не является уравнением; 8) p = 114.29 (приблизительно); 9) x = 9; 10) y = 4; 11) x = 64; 12) y = 3.6