Решебник по математике 6 класс Ерина Никольский рабочая тетрадь Часть 1, 2 Часть 1 | Страница 14

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\[\textbf{а)}\ 96\ :72 = 4x\ :21\]

\[4x \cdot 72 = 96 \cdot 21\]

\[x = \frac{96 \cdot 21}{4 \cdot 72} = \frac{12 \cdot 21}{4 \cdot 9} = \frac{3 \cdot 7}{3}\]

\[x = 7.\]

\[Ответ:7.\]

\[\textbf{б)}\ \frac{9}{25}\ :\frac{4x}{5} = \frac{21}{20}\ :\frac{63}{100}\]

\[0,8x \cdot 1,05 = 0,36 \cdot 0,63\]

\[x = \frac{0,36 \cdot 0,63}{0,8 \cdot 1,05} = \frac{0,12 \cdot 0,63}{0,8 \cdot 0,35} =\]

\[= \frac{0,3 \cdot 0,9}{0,2 \cdot 0,5}\]

\[x = 0,27.\]

\[Ответ:0,27.\]

\[\textbf{в)}\ \frac{x + 1}{16} = \frac{3}{14}\]

\[14 \cdot (x + 1) = 16 \cdot 3\]

\[14x + 14 = 48\]

\[14x = 48 - 14\]

\[14x = 34\]

\[x = \frac{34}{14} = \frac{17}{7}\]

\[x = 2\frac{3}{7}.\]

\[Ответ:2\frac{3}{7}.\]

\[\textbf{г)}\ x\ :\frac{8}{15} = 9\frac{3}{4}\ :17\frac{1}{3}\]

\[17\frac{1}{3}x = \frac{8}{15} \cdot \frac{39}{4}\]

\[\frac{52}{3}x = \frac{78}{15}\]

\[x = \frac{26}{5}\ :\frac{52}{3}\]

\[x = \frac{26}{5} \cdot \frac{3}{52}\]

\[x = \frac{3}{10}\]

\[x = 0,3.\]

\[Ответ:0,3.\ \]

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\[\frac{5}{8} = \frac{20}{x}\]

\[5x = 160\]

\[x = 160\ :5\]

\[x = 32\ (г) - серебра\ в\ сплаве.\]

\[20 + 32 = 52\ (г) - масса\ \]

\[сплава.\]

\[Ответ:52\ г.\]

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\[5\frac{3}{5}\ :1\frac{3}{5} = x\ :1\frac{1}{7}\]

\[1\frac{3}{5}x = \frac{8}{7} \cdot \frac{28}{5}\]

\[x = \frac{8 \cdot 4 \cdot 5}{8 \cdot 5}\]

\[x = 4\ (м) - высота\ зала.\]

\[Ответ:4\ м.\]