17.
a)
[tex]0 < \frac{a}{20} < \frac{1}{4}\\\\\frac{0}{20} < \frac{a}{20} < \frac{5}{20}\\\\0 < a < 5\\\\\underline{a \in \{1, 2, 3, 4\}}\\\\\\0 < \frac{b}{15} < \frac{1}{2}\\\\\frac{0}{30} < \frac{2b}{30} < \frac{15}{30}\\\\0 < 2b < 15 \ \ /:2\\\\0 < b < 7,5\\\\\underline{b \in \{1, 2, 3, 4, 5, 6, 7\}}[/tex]
[tex]\frac{1}{2} < \frac{c}{21} < 1\\\\\frac{21}{42} < \frac{2c}{42} < 21 \ \ /:2\\\\10,5 < c < 21\\\\\underline{c \in \{11, 12, 13, 14, 15, 16, 17, 18, 19, 20\}}\\\\\\1 < \frac{d}{30} < 1\frac{1}{2}\\\\1 < \frac{d}{30} < \frac{3}{2}\\\\\frac{30}{30} < \frac{d}{30} < \frac{45}{30}\\\\30 < d < 45\\\\\underline{d \in\{31, 32, 33,34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44\}}[/tex]
b)
[tex]\frac{1}{7} < x < \frac{2}{7}\\\\\frac{2}{14} < x < \frac{4}{14}\\\\\underline{np. \ x = \frac{3}{14}}\\\\\\\frac{3}{4}< y < \frac{7}{8}\\\\\frac{12}{16} < y < \frac{14}{16}\\\\\underline{np. \ y = \frac{13}{16}}[/tex]
[tex]\frac{1}{3} < z < \frac{1}{2}\\\\\frac{2}{6} < z < \frac{3}{6}\\\\\frac{4}{12} < z < \frac{6}{12}\\\\\underline{np. \ z = \frac{5}{12}}\\\\\\\frac{2}{3} < w < \frac{3}{4}\\\\\frac{8}{12} < w < \frac{9}{12}\\\\\frac{16}{24} < w < \frac{18}{24}\\\\\underline{np. \ w = \frac{17}{24}}[/tex]
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